Study of flow induced vibration of a circular cylindrical structure
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This document summarizes a student's study of flow induced vibration of a circular cylindrical structure. It includes calculations of the cylinder's properties and natural frequencies. It then discusses practical applications of vortex induced vibration including failures of structures like bridges. It notes multibody effects are important in applications like heat exchangers where multiple tubes can vibrate together. Methods for suppressing vortex induced vibration on cylinders are also listed.
Study of flow induced vibration of a circular cylindrical structure
- 1. Study of Flow Induced Vibration of a Circular Cylindrical Structure NAME : Dilshan K.M.G.L. COURSE : BSc. Engineering INDEX NO. : 150131A DATE OF PER. : 11.05.2018 DATE OF SUB. : 25.05.2018
- 2. Calculation Mass of the cylinder (M) = 358.28𝑔 Length of the cylinder (L) = 0.57𝑚 Circumference of the cylinder (C) = 0.29𝑚 Diameter of the cylinder (D) = 𝐶 𝜋 = 0.29 𝜋 = 0.0923𝑚 Spring stiffness = 𝑊 ∆𝑙 = 0.089565 ×9.81 𝑁 (95−75) 𝑚𝑚 = 0.044 𝑁/𝑚𝑚 Spring Initial length (mm) Final length (mm) Applied weight (g) Spring stiffness (N/mm) 1 75 95 89.565 0.043931633 2 77 110 89.565 0.026625232 3 77 104 89.565 0.03254195 4 76 112 89.565 0.024406463 Spring stiffness = ∑ 𝐾 4 = 0.044 +0.027+0.033+0.024 4 = 0.030 𝑁/𝑚𝑚 Moment of inertia of the cylinder 𝐼 = 1 4 𝑀𝑅2 + 1 12 𝑀𝐿2 𝐼 = 1 4 × 0.358 × 0.04622 + 1 12 × 0.358 × 0.572 = 0.009891𝑘𝑔𝑚2 First natural frequency 𝑓1 = 1 2𝜋 √ 𝐾 𝑀 𝑓1 = 1 2𝜋 √0.03 ×106 358 .28 = 1.446 𝑠−1 Second natural frequency 𝑓1 = 𝑙 4𝜋 √ 𝐾 𝐼 𝑓1 = 0.57 4𝜋 √ 0.03×106 9.89 = 2.481 𝑠−1
- 3. Discussion Practical applications of vortex induced vibration Vortex induced vibration can be simply demonstrated using this experiment, flow around cylinder. Here because of the excessive curvature, at some point on the cylinder, flow will separate from the surface on the cylinder and then vortices will have generated. That will be caused by the pressure difference between upstream and downstream flow. Since vortices are not symmetric around the axis of the cylinder, lift force generated by the vortices are not symmetric, thus there will be resultant force always to one side, either up or down. So that cylinder tends to vibrate at a frequency. Vortex induced vibration (VIV) is affected to different branch of engineering fields, from cables to exhaust pipe arrays. That is very important when structures near to costal areas because of the tide and high wind speed directly entangle with the structure. VIV is important to buildings structures as well as moving solid bodes. There are plenty of examples in the vicinity that was designed and build considering the VIV effect. Basically, VIV strongly important to slender structural components like towers that had lower cross-sectional areas relative to the height of that. Offshore platforms, bridges, heat exchangers, marine cables, towed cables, pipelines, and also many hydrodynamic and hydrodynamic based applications is affected with the VIV. Most of the times the structure gets failed because of the fatigue failure, that is happened due to cyclic loads. VIV produced unsymmetrical forces along the vibrating axis caused for the fatigue failure. There are some engineering applications that collapsed due to VIV effect such as Tacoma Narrows Bridge. That failure is occurred due to the fatigue failure, due to oscillating forces. Another structure is John Hancock Building in Boston. That building covered using black glasses and most of the glasses were broken without no reason. And also, after completing the construction, most of the window glasses in other offices near that building were shattered. Engineers thought that was due to high speed wind. But finally discovered that is happened due to VIV. Another thing is that building is not bend along the vertical axis but tends to twist along the central axis. Because of the structural components were unbearable torsion and there was threat to deform. So, engineers had to add counter masses on the bottom floor to reduce the twisting moment. That twisting also happened due to VIV effect. And also, structural platforms in the drilling and production risers in petroleum production is affected by the VIV from two ways. Hydrodynamic forces and aerodynamic forces. Structures under the sea is affected by the hydrodynamic forces and thin tubes on the platform is affected by the aerodynamic forces. There are several types of platforms in petroleum production. Most of the platforms can be categorized under fixed rigs, tension leg, spar platforms. In fixed rigs platforms, structure is connected to the bottom of the sea permanently. The thin structure connected each other. That structure has higher resistance to vibration than other kind of platforms. So that hydrodynamic effect is not much affected. In tension leg platforms, structed is anchored using several counter masses. That cables must be arranged considering VIV effect due to solid body interaction. In spar platform, there is only one beam that connected the structure to the ground. So that tidal waves can be affected on the body.
- 4. Importance of multibody effect in practice In the heat exchangers, the arrangement of the tubes in the space must be planed considering VIV effect. Steam, vaporized water is passing through the tubes so that tubes will get vibrate because steam particles collapse with the wall of the tube. When there are several tubes along each other, resonance can be induced. The tubes are not vibrating in same frequency because the velocities of the steam can be varying. So that vibration of a tube can be affected to another tube and also situation can be benefitted or can get disaster. If the arrangement is in the way that reduce the VIV effect, the possibility fatigue failure is reduced and fatigue life is increased. But the positions are in the way the increase the frequency of vibration, the fatigue life can be decreased and final result will be catastrophic. Here the frequencies of the vibration are varying along the cable and also frequency shedding can be changed. So that nodes can be generated on the cable but the nodes are not stable. That also caused to increase the fatigue failure. Another example can be explained using tension leg platform in the petroleum production in the middle of the sea. Previous example is due to aerodynamics and this one is based on the hydrodynamics. Here the platform is anchored to the bottom of the sea and for one anchor has several cables. The arrangement of the cable must be designed using within single anchor and among other anchors. VIV increases the effective drag coefficient due to increment of pressure forces. Also, that introduced another drag coefficient called fluctuating drag coefficient. The large towers such as chimneys in coal power plants, are affected by there drag forces and also that will tend to bend the structure and twist. The flexibility of the structure must be slightly increased due to that effect, otherwise that will tend to collapse. There are several methods that can used to suppression of the VIV on cylindrical objects. 1. Helical strake 2. Shroud 3. Axial slats 4. Streamline fairing 5. Splitter plate 6. Ribboned cable 7. Pivoted guiding vane 8. Spoiler plates
- 5. Reference FUNDAMENTALS OF VORTEX-INDUCED VIBRATION. (2015). Retrieved from Bureau of Safety and Environmental Enforcement: https://www.bsee.gov/sites/bsee.gov/files/tap-technical- assessment-program//485ab.pdf Kim, K.‐ P. Y.‐ M. (2017, July 27). The evaluation of wind‐ induced vibration responses to a tapered tall building. Retrieved from Wiley online library: https://onlinelibrary.wiley.com/doi/pdf/10.1002/tal.371 Techet, A. (2005). Vortex Induced Vibatiob. Retrieved from MIT: http://web.mit.edu/13.42/www/handouts/reading-VIV.pdf
- 6. y = 0.0538x - 2.2751 0 2 4 6 8 10 12 50 70 90 110 130 150 170 190 210 230 Velocity(m/s) Counter value Velocity vs Counter Value