Page 266 - Pressure Vessel Design Manual

244 Pressure Vessel Design Manual

PROCEDURE 4-8
VIBRATION OF TALL TOWERS AND STACKS 117-271

Tall cylindrical stacks and towers may be susceptible to c. Liquid holdup and sloshing.
wind-induced oscillations as a result of vortex shedding. d. Soil.
This phenomenon, often referred to as dynamic instability, e. Foundation.
has resulted in severe oscillations, excessive deflections, f. Shell material.
structural damage, and even failure. Once it has been deter- g. External insulation.
mined that a vessel is dynamically unstable, either the vessel
must be redesigned to withstand the effects of wind-induced
oscillations or external spoilers must be added to ensure that Damping Mechanisms
vortex shedding does not occur.
The deflections resulting from vortex shedding are per- Internal linings are also significant for damping vibration;
pendicular to the direction of wind flow and occur at rela- however, most tall, slender columns are not lined, whereas
tively low wind velocities. When the natural period of many stacks are. The lining referred to here would be the
vibration of a stack or column coincides with the frequency refractory type of linings, not paint, cladding, or some pro-
of vortex shedding, the amplitude of vibration is greatly mag- tective metal coating. It is the damping effect of the concrete
nified. The frequency of vortex shedding is related to wind that is significant.
velocity and vessel diameter. The wind velocity at which the Damping is the rate at which material absorbs energy
frequency of vortex shedding matches the natural period of under a cyclical load. The energy is dissipated as heat from
vibration is called the critical wind velocity. internal damping within the system. These energy losses are
Wind-induced oscillations occur at steady, moderate wind due to the combined resistances from all of the design fea-
velocities of 20-25 miles per hour. These oscillations com- tures mentioned, Le., the vessel, contents, foundation, inter-
mence as the frequency of vortex shedding approaches the nals, and externals. The combined resistances are known as
natural period of the stack or column and are perpendicular the damping factor.
to the prevailing wind. Larger wind velocities contain high- The total damping factor is a sum of all the individual
velocity random gusts that reduce the tendency for vortex damping factors. The damping factor is also known by
shedding in a regular periodic manner. other terms and expressions in the various literature and
A convenient method of relating to the phenomenon of equations and expressed as a coefficient. Other common
wind excitation is to equate it to fluid flow around a cylinder. terms for the damping factor are damping coeflicient, struc-
In fact this is the exact case of early discoveries related to tural damping coefacient, percent critical damping, and
submarine periscopes vibrating wildly at certain speeds. At material damping ratio. In this procedure this term is
low flow rates, the flow around the cylinder is laminar. As the always referred to either as factor DF or as /?.
stream velocity increases, two symmetrical eddies are formed There are eight potential types of damping that affect a
on either side of the cylinder. At higher velocities vortices structure’s response to vibration. They are divided into three
begin to break off from the main stream, resulting in an major groups:
imbalance in forces exerted from the split stream. The dis-
charging vortex imparts a fluctuating force that can cause Resistance:
movement in the vessel perpendicular to the direction of Damping from internal attachments, such as trays.
the stream. Damping from external attachments, such as ladders,
Historically, vessels have tended to have many fewer inci- platforms, and installed piping.
dents of wind-induced vibration than stacks. There is a vari- Sloshing of internal liquid.
ety of reasons for this:
Base support:
Soil.
1. Relatively thicker walls.
2. Higher first frequency. Foundation.
3. External attachments, such as ladders, platforms, and Energy absorbed by the shell (hysteretic):
piping, that disrupt the wind flow around the vessel. Material of shell.
4. Significantly higher damping due to: Insulation.
a. Internal attachments, trays, baffles, etc. Internal lining.
b. External attachments, ladders, platforms, and Karamchandani, Gupta, and Pattabiraman give a detailed
piping. account of each of these damping mechanisms (see Ref. 17)