This document summarizes research on vortex shedding and its effects on tall, cylindrical structures. It defines vortex shedding as alternating low pressure zones that form on the downwind side of a structure due to wind, causing vibrations. These vibrations can be damaging if they match the structure's natural frequency. The document outlines methods for analyzing the risk of vortex shedding, including calculating the vortex shedding frequency and comparing it to the structure's natural frequencies. It also discusses ways to address vortex shedding in design, such as adding strakes or changing the structure's geometry.

1. Study of Column Vibration
MBO Assignment
Prepared By: - Anup kumar Singh
11/5/2015

2. Page 2 of 7
Item
No.
Table of Contents
1 Introduction
2 What is vortex shedding
3 Definitions of Important terms in Vortex Shedding analysis
4 Why does Vortex Shedding Matter
5 Probability of occurrence & requirement of vibration analysis
6 How to Calculate Vortex Shedding
7 Conclusion
8 References

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Introduction:-
This study is primarily concerned with the vibration of vertical pressure vessels known as columns or towers.
We will discuss following topics related to vortex shedding:
 What is vortex shedding
 Definitions of Important Terms
 Why does vortex shedding matter
 Probability of occurrence & requirement of vibration analysis
 How to calculate vortex shedding
What is vortex shedding:
Vortex shedding happens when wind hits a structure, causing alternating vortices to form at a certain
frequency. This in turn causes the system to excite and produce a vibrational load. Historically, it has been
very difficult to calculate by hand. Today, with modern technology and new engineering practices, vortex
shedding analysis is a valuable tool used in the design of tall equipment and structures.
If we are designing a tall, slender, structure and it is subject to wind, we need to consider vortex shedding
Vortex Shedding is the instance where alternating low pressure zones (blue colors in figure below) are
generated on the downwind side of the column, as shown in the figure below which showing vortex shedding
phenomenon induced by wind flowing over a cylindrical column.
These alternating low pressure zones cause the column to move towards the low pressure zone, causing
movement perpendicular to the direction of the wind. When the critical wind speed of the column is reached,
these forces can cause the column to resonate where large forces and deflections are experienced. Vortex
shedding is a complex physical phenomenon, especially when it degenerates into lock-in condition. As large
vibrations may occur at moderate and frequent wind velocities, structures may undergo a great number of
stress cycles that lead to damage accumulation and may determine structural failure without exceeding the
ultimate limit stress. Considering the potential vortex shedding fatigue induced damage it is very important
the design procedures to account in a realistic manner for the vortex shedding dynamic induced loads.
Definitions of Important terms in Vortex Shedding analysis:-
 Critical wind velocity (Vc): The velocity at which the frequency of vortex shedding matches one of
the normal modes of vibration

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 Logarithmic decrement (δ): Logarithmic decrement is the log of the ratio of successive amplitudes of
damped, freely vibrating structure and is a measure of the structural ability of the stake or tower to
dissipate energy during vibration. For a particular structure δ depends on the type of construction and
lining used.
 Static deflection: Deflection due to wind or earthquake in the direction of load.
 Dynamic deflection:Deflection due to vortex shedding perpendicular to the direction of the wind.
 Lock-in: A cylinder is said to be “locked in” when the frequency of oscillation is equal to the
frequency of vortex shedding. In this region the largest amplitude oscillations occur.
Why does Vortex Shedding Matter:
The frequency of the vortices is dependent on the shape of the body, and the velocity of the fluid flow or wind
hitting this body. The vortices create low pressure zones on the downwind side of the object on alternate sides.
As the fluid flows to fill the low pressure zone, it produces a vibration at a specific calculable frequency. This
vibration is only a major concern if it happens to coincide with the natural frequency of the structure.
The wind velocity at which the frequency of vortex shedding matches the natural period of vibration is called
the critical wind velocity. Wind-induced oscillations occur at steady, moderate wind velocities of 20-25 miles
per hour. These oscillations commence as the frequency of vortex shedding approaches the natural period of
the stack or column and are perpendicular to the prevailing wind. Larger wind velocities contain high velocity
random gusts that reduce the tendency for vortex shedding in a regular periodic manner.
For structures that are tall and uniform in size and shape, the vibrations can be damaging and ultimately lead
to fatigue failure. Towers/Columns are highly susceptible to vibrations induced by vortex shedding. By
completing a vortex shedding analysis of structures under wind loading, we can evaluate whether more
efficient structures can and should be developed.
Probability of occurrence & requirement of vibration analysis:
Once a vessel has been designed statically, it is necessary to determine if the vessel is susceptible to wind-
induced vibration. Historically, the thumb rule was to do a dynamic wind check only if the vessel L/D ratio
exceeded 15 and the POV (Period of Vibration) was greater than 0.4 seconds. This criterion has proven to be
unconservative for a number of applications. In addition, if the critical wind velocity, Vc, is greater than 50
mph, then no further investigation is required. Wind speeds in excess of 50mph always contain gusts that will
disrupt uniform vortex shedding.
The above mentioned criteria may give first impression regarding stability of structure under vortex shedding,
but to ensure with more certainty structure shall be checked with following criterion:
Criterion 1
 If W/LDr2 < 20, a vibration analysis must be performed
 If 20< W/LDr2 < 25, a vibration analysis should be performed
 If W/LDr2 > 25, a vibration analysis need not be performed
Criterion 2
 If Wδ/LDr2 < 0.75, the vessel is unstable.
 If 0.75 < Wδ/LDr2 < 0.95, the vessel is probably unstable.
 If Wδ/LDr2 > 0.95, the vessel is stable

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Limitations of the above criterion are that it should be restricted to cylindrical steel cantilevered structures
having fairly uniform distribution of non-stiffness masses and width Lc /L ratios less than 0.5, (D/L2) (10)4
less than eight, W/Ws ratio not exceeding six.
Where;
W :- Total weight of structure in lb
Ws :- Weight of structure excluding weight of parts which do not contribute to stiffness, lb
L :- Total length of structure, ft
Lc:- Total length of conical sections of structure, ft
D :- Average internal diameter of structure, ft
Dr: - Average internal diameter of top half of structure, ft
δ: - Logarithmic decrement
WF = Wδ/LDr2:- Damping factor
How to Calculate Vortex Shedding:-
Step 1: Determine the Vortex shedding Frequency
The vortex street frequency is calculated using the Reynolds number (which describes the fluid flow
characteristics) and the Strouhal number (which describes the oscillations of a fluid). The Reynolds number is
calculated using viscosity, density, flow velocity, and some geometry from the object in the fluid. It is
calculated over a range of flow speeds (or wind velocities). The Strouhal number is then calculated from those
Reynolds numbers, although for laminar flow situations a Strouhal of 0.2 is often used. The frequency of the
vortex street is then calculated using the Strouhal number, the width of the body, and the flow speed.
Re = VD /ν
Where:
Re = Reynolds number;
V= wind speed [m/s];
D= Structure diameter [m];
ν = kinematic viscosity [m2
/s].
Fluid characteristics’ in Reynolds number:-
Sub critical Range: Re < 3x105
Critical Range: 3x105 ≤ Re ≤ 3x106
Trans critical Range: Re > 3x106
Strouhal number:-
Subcritical (Re < 3x105): 0.18 (for circular cross section)
Supercritical and Trans critical (Re > 3x105): 0.25 (for circular cross section)
Vortex Shedding Frequency:-
fs = SV/ D
Where
fs = Vortex shedding frequency
S= Strouhal number
D= Structure diameter

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Step 2: Find the natural frequencies of the mechanical system
For the complex geometry of columns with the varying diameters, thickness and materials. In the past, finding
the correct mathematical model of such a structure in order to find the natural frequency would be difficult
and inaccurate. Today, with the advancement of technology and engineering practice, calculating the natural
frequency can be done fairly efficiently. Finite Element Analysis software such as Solid Works’ Simulation
Package can be used to calculate the natural frequency of a very complex system.
Step 3: Comparing Natural frequencies to calculated frequencies
Now that we have the natural frequencies of the mechanical system, we can compare these frequencies to the
vortex shedding frequencies as calculated in step 1. If the natural frequency line up to the vortex shedding
frequencies calculated in stage 1 and the wind speed scenarios, it is highly likely column could have a
problem for its stability. It is important to apply sound engineering judgment at this stage when interpreting
the results. The formulas used in this calculation are only good for a certain rage of wind speeds and to some
degree are based on experimental data. The accuracy of the analysis also depends on how accurate of a model
is used for analysis. There are several steps we can take in order to prevent vortex shedding.
Step 4: Fixing the problem
There are three main approaches that can be applied to prevent the structural failure from vortex shedding.
The simplest is to address the fluid flow and create a disturbance on the structure so that the vortex street
cannot form. This is commonly done by adding a spiral at the top of the structure (but any change to the body
that disrupts the vortex would work). Another method is to design the structure itself so the natural
frequencies are outside the operating frequencies. This can be done by varying the cross-section along the
length of the structure or by adding or changing supports. There are also dynamic systems such as dampeners
that can successfully be applied to absorb vibration.
While vortex shedding is a common phenomenon that can lead to structural failure, it is one that is often
overlooked because of the complexity of modeling the situation correctly. Using the steps outlined above,
vibrational problems can be easily identified and a few hypotheses can be tested. Design changes can be made
before any real problem arises. The key point to remember is if we are designing a tall slender mechanical
system exposed to wind loading, make sure that we are considering vortex shedding vibrations and conducts
the appropriate analysis.
The following design modifications may be made to the vessel to eliminate vortex shedding:
 Add thickness to bottom shell courses and skirt to increase damping and raise the POV.
 Reduce the top diameter where possible.
 For stacks, add helical strakes to the top third of the stack only as a last resort. Spoilers or strakes
should protrude beyond the stack diameter by a distance of d/12 but not less than 2 in.
 Cross-brace vessels together.
 Add guy cables or wires to grade.
 Add internal linings.
 Reduce vessel below dynamic criteria.
The following precautions should be taken for structure susceptible for Vortex Shedding:-
 Include ladders, platforms, and piping in your calculations to more accurately determines the natural
frequency.
 Grout the vessel base as soon as possible after erection while it is most susceptible to wind vibration.
 Add external attachments as soon as possible after erection to break up vortices.
 Ensure that tower anchor bolts are tightened as soon as possible after erection.

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CONCLUSION:-
The design method to be used for vertical pressure vessels depends on whether the longitudinal stress in the
shell is tension or compression, and on whether the vessel is subjected to internal or external pressure. Self-
supporting vertical pressure vessels should always be investigated regarding their possible behavior under
vibrating conditions. The evaluation of wind velocity effects should include considerations pertaining to the
distribution of external vessel attachments as well as the surrounding equipment and terrain. It should be
borne in mind that liquid loading in vessels having trays will help dampen vibration, but should not be relied
upon as a cure all. If vibration trouble does occur, careful analysis of any proposed remedy must be made in
order to avoid trouble from some other source. External loads applied to vertical pressure vessels produce
axial loading and bending moments on the vessel. These result in axial tensions and compressions in the shell,
which must be combined with the effects of the pressure loading to give the total longitudinal stress acting in
the shell.
REFERENCES:-
 Lecture: Prof. A. H. Techet
 International Journal of Mechanical Engineering and Technology (IJMET), ISSN
 Structural Vortex Shedding Response Estimation Methodology and Finite Element Simulation:
I. Giosan, P.Eng.
 PVD Manual: Dennis Moss