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FUNDAMENTALS OF VORTEX-INDUCED VIBRATION By Charles Dalton University of Houston

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Figure Citations

Fig. 1 Panton, R., Incompressible Flow, 3rd Ed., Wiley, 2005 Fig. 2 Blevins, Flow Induced Vibration, 2nd Ed.. Van Nostrand Reinhold, 1990 Fig. 3 Blevins, Flow Induced Vibration, 2nd Ed.. Van Nostrand Reinhold, 1990 Fig. 4 Szepessy, S., Bearman, P. JFM, 1992 Fig. 5 Blevins, Flow Induced Vibration, 2nd Ed.. Van Nostrand Reinhold, 1990 Fig. 6 Dalton, C. unpublished, 1998 Fig. 7 Norberg, C., Personal Communication, 2002 Fig. 8 Blevins, Flow Induced Vibration, 2nd Ed.. Van Nostrand Reinhold, 1990 Fig. 9 Williamson, C.H.K., Roshko, A., JFS, 1988 Fig. 10 Williamson, C.H.K., Roshko, A., JFS, 1988 Fig. 11 Blevins, Flow Induced Vibration, 2nd Ed.. Van Nostrand Reinhold, 1990 Fig. 12 Sarpkaya, T., JFS, 2004 Fig. 13 Khalak, A., Williamson, C.H.K., JFS, 1999 Fig. 14 Sarpkaya, T., JFS, 2004 Fig. 15 Sarpkaya, T., JFS, 2004 Fig. 16 Sarpkaya, T., JFS, 2004 Fig. 17 Sarpkaya, T., JFS, 2004 Fig. 18 Sarpkaya, T., JFS, 2004 Fig. 19 Sarpkaya, T., JFS, 2004 Fig. 20 Sarpkaya, T., JFS, 2004 Fig. 21 Sarpkaya, T., JFS, 2004 Fig. 22 Sarpkaya, T., JFS, 2004 Fig. 23 Sarpkaya, T., JFS, 2004 Fig. 24 Sarpkaya, T., JFS, 2004 Fig. 25 Blevins, Flow Induced Vibration, 2nd Ed.. Van Nostrand Reinhold, 1990 Fig. 26 Dalton, C. et al., JFS, 2001 Fig. 27 Dalton, C. et al., JFS, 2001

Presentation Notes: This page is a series of questions that introduce the audience to the subject of VIV in a uniform and comprehensive manner. Discussion of these questions and their answers assures that everyone has the same comprehensive understanding of what VIV is and why and when it occurs. Questions What is VIV? What are the details of a steady approach flow past a stationary cylinder? o To understand VIV, you must first understand the physics of a steady approach flow past a nonvibrating circular cylinder. How and why does VIV occur? What kind of body shapes experience VIV? What kinds of VIV are there? o Self-excited oscillations - this type of VIV is what occurs naturally, i.e., when the vortex-shedding frequency and the natural frequency are approximately the same. (This is the real VIV this is vortex-induced vibration) o Forced oscillations occurs at velocities and amplitudes which are preset and can be controlled independently of fluid velocity. (This is not the real VIV this is vibration-induced vortices). How do you eliminate VIV? o This is the ultimate question! It may be best to design around VIV. In other words, lets learn how to predict VIV and then avoid the situations that will produce VIV. The circular cylinder will always be the preferred shape and the fluctuating lift will always be there, VIV or no VIV. Since we cant avoid the shedding of vortices, lets try to learn to avoid the situations that produce VIV.

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Presentation Notes: These next two pages contain a detailed Nomenclature for the VIV problem. This Nomenclature is suggested by Sarpkaya in an attempt to provide uniformity to the VIV literature. NOMENCLATURE fvac the natural frequency of a system as found in a vacuum. fex the frequency of oscillation of a vibrating body (either forced or Self-excited) regardless of whether lock-in is present. fSt the vortex shedding frequency (Strouhal frequency) of a body at Rest. fvs the vortex shedding frequency of a body in motion (forced or self excited). In the lock-in range, fvs becomes increasingly smaller than fSt until lock-out. Re the Reynolds number (= Ud/v), the ratio of inertia forces to viscous forces. St the Strouhal number (=fStd/U), the dimensionless vortex Shedding frequency. KC Keulegan-Carpenter number (=UmaxT/d = Umax/fexd) Vr the reduced velocity (=U/fexd), the approach velocity normalized The the excitation frequency and the diameter. StVr - the product of the Strouhal number and the reduced velocity (=(fStd/U)(U/fexd) = fSt/fex) 1/(StVr) equals fex/fSt

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fair the natural frequency of a system in air. fwtr the natural frequency of a system in water. material damping (not fluid damping). m* - reduced mass, = ((mb/l)/ f d2/4) or m*= m/b with m =(mb/l)/(d2/4) . VIV body a geometric shape, not necessarily a cylinder or even a circular cylinder, which will produce VIV. m* the mass-damping term. A/d the amplitude to diameter ratio. CD Drag Coefficient, CD = D/f Ap lU /2 CL Lift Coefficient, CL = L/f Ap lU /2 CM Inertia Coefficient, CM = FI/(fVol dU/dt) Added Mass the increase in effective mass that occurs when the acceleration of a body is nonzero. This is also called the hydrodynamic mass. The inference is that the effective mass is the sum of the mass of the body and the added mass. The added mass doesnt influence the situation until there is acceleration.2 2

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Presentation Notes: Figure 1 is a plot of the drag coefficient (Cd) versus Reynolds number (Re) for a steady approach flow past a circular cylinder. Figure 2 is a schematic diagram which shows the various regimes of the flow past a circular cylinder. These two figures are discussed simultaneously so that the meaning of the various aspects of the drag-coefficient/Reynolds-number plot can be fully understood. Figure 1: Flow around a circular cylinder

Drag and Curve for a cylinder. Data is from Delany and Sorenson (1953), Finn (1953), Roshko (1961), Tritton (1959) and Wieselsberger (1921)

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Figure 2: Regimes of fluid flow across smooth circular cylinders (Lienhard, 1966)

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Presentation Notes: This figure is a plot showing the Strouhal number (St, St=Dfvs/U) versus the Reynolds number (Re, Re=UD/). The variation of St with Re is discussed so that the audience has an understanding of what flow features influence St, i.e., the vortex shedding frequency, and why they do so. Figure 3: Strouhal number Reynolds number relationship for circular cylinders

(Lienhard, 1966; Achenbach and Heinecke, 1981). S 0.21 (1-21/Re) for 40