Structural Integrity

1. N-1300 ASME appendix N

2. Outline
 Main definitions
 Vortex shedding
 Synchronization
 Design procedure for cylinders
 Fluid elastic instability
 Critical velocity
 Design considerations
 Field of application
 Vibration damage in HE

3. Main definitions
 Fluid forces :
 Fluid excitation forces are created by the incident flow
on a structure
 Fluid-structure coupling forces are induced by structural
motion
 Added mass and added damping:
 Increase the effective mass and damping of a structure
vibrating in a fluid.
 the presence of a dense fluid adjacent structures can
couple their vibrations
 function of the geometry of the structural surface
exposed to fluid and the presence of adjacent structures

5.  Weakly coupled fluid Structure system:
 The FIV excitation mechanism causes small structural
motion
 Fluid forces induced by the structural motion can be
linearly superimposed onto the fluid excitation forces
 Examples flow turbulence and turbulent boundary
layers over rods, plates, and shells
 Strongly coupled fluid‐structure system:
 The FIV excitation mechanism causes the structural
motion to become large enough to change the flow field
 Some of the fluid forces amplify
 In general, the coupling forces are highly nonlinear
functions of structural motion and flow velocity

6. Vortex Shedding
 For ideal cross flow, where a long, smooth surface tube is
isolated in uniform (2–D) cross flow with little or no
turbulence in the approaching flow stream.
 These vortices produce alternating lift forces normal to the
tube axis and flow and are nearly as large as the steady
 Vortex shedding in the wake of a tube in cross flow
produces both fluid excitation forces and fluid‐structure
coupling forces that amplify structural motion.

8.  If the vortex shedding frequency is sufficiently different
from the structural natural frequencies, the alternating lift
forces act as fluid excitation forces only.
 However, if the vortex shedding frequency and one of the
structural natural frequencies are sufficiently close to each
other and the fluid excitation forces can produce large
motions.
 Enough experimental data are available to bound the fluid
excitation forces,
 but the representation of the coupled fluid‐structure forces
is still being researched
 the frequency in hertz of the alternating lift force can be
expressed as:
S = Strouhal number
V = mean velocity
D = cylinder diameter

9. Vortex shedding in cylindrical bluff bodies
 The following discussions are based on the circular
cylinder; however, the concepts apply equally well to other
bluff bodies.
 The oscillating lift force on single cylinder of diameter D
and length L
• where CL, fs , and J are functions of the Reynolds number Re
and must be determined experimentally.
CL = lift coefficient
J2 = joint acceptance
q = dynamic pressure = ρV2
fs = frequency of vortex shedding
t = time

10. Flexible cylinders
 Off resonance condition occurs when vortex shedding
frequency fs is sufficiently different from the structural
natural frequencies
 Shedding lift force by F is valid, and is conservative if CL = 1
and J = 1 is chosen.
 Normally, off‐resonance response is small.
 For a spring‐supported cylinder in an air stream,
synchronization depends upon the damping parameter,
mtδn/ρD2.
 The ordinate, V/f n D, is a reduced velocity, where f n is the
natural frequency of the spring‐mounted cylinder.
 In Figure N-1323-1, the shaded area is the region of
synchronization.
 no synchronization occurs for mt δn/ρD2 > 32

11. Figure N-1323-1
Synchronization of the Vortex Shedding Frequency and the Tube Natural
Frequency for a Single,
Flexibly-Mounted Circular Cylinder

12. Design Procedures for a Circular Cylinder
Resonant operating conditions should be avoided, but
complex designs often make this impossible.
avoided by four methods:
1. If the reduced velocity for the fundamental vibration mode
(n = 1) satisfies
2. Reduced damping should be:

13. Where:
ξn = δn/2π is the fraction of critical damping measured in air
Generalized mass =
with ϕn the nth mode shape function and mt (x) is the
cylinder mass per unit length.
3. If for a given vibration mode
then lift direction lock‐in is avoided and drag direction lock‐in
is suppressed.
4. If the structural natural frequency falls in the ranges
fn < 0.7f s or f n > 1.3f s

14. FLUID-ELASTIC INSTABILITY
 As flow velocity increases, a critical value is attained at
which a large increase in response occurs.
 Continued increases in the supplied energy results in
continued static or dynamic divergence
 The resultant strong fluid‐structure coupling excitation
forces fall into several groups
 forces that vary approximately linearly with
displacement of a tube from its equilibrium position
(displacement mechanisms)
 Fluctuations in the net drag forces induced by the
oscillating tube’s relative velocity with respect to the
mean flow (fluid damping mechanism) .
 Combination of both

15.  The general characteristics of tube vibration during
instability are as follows.
 Tube Vibration Amplitude. Once a critical cross flow
velocity is exceeded, vibration amplitude increases very
rapidly with flow velocity V, usually as Vn where n = 4 or
more, compared with an exponent in the range 1.5 < n < 2.5
below the instability threshold.
 This can be seen in Figure N-1331-1, which shows the
response of an array of metallic tubes to water flow. The
initial hump is attributable to vortex shedding that tends to
produce larger amplitudes in water flow than air flows.
 Vibration Behavior With Time. Often the large amplitude
vibrations are not steady in time, but rather beat with
amplitudes rising and falling about a mean value in a
pseudorandom fashion

16. Figure N-1331-1 Response of a Tube Bank to Cross
Flow

17.  Synchronization Between Tubes. Most often the tubes move
with neighboring tubes in somewhat synchronized orbits,
as shown in Figure N-1331-2. This behavior has been
observed in tests both in water and air. As the tubes whirl
in their oval orbits they extract energy from the fluid.
Figure N-1331-2
Tube Vibration Patterns at Fluid-Elastic Instability for a Four-Tube Row

18.  Influence of Structural Variations. Restricting the motion
or introducing frequency differences between one or more
tubes often increases the critical velocity for instability
(max 40%).

19. Prediction of the Critical Velocity
 Dimensional analysis considerations imply that the onset
of instability is governed by the following dimensionless
groups:
 the mass ratio mt /ρD2
 the reduced velocity V/fD
 the damping ratio ξ n, measured in the fluid
 The pitch to diameter ratio P/D
 the array geometry (see Figure N-1331-3)
 Reynolds number VD/ν.

21.  for most cases, the flow is fully turbulent (VD/ν > 2000)
and the Reynolds number is not expected to play a major
role in the instability.
 One general form that has been used to fit experimental
data is
• where C and the indices a and b are functions of the tube
array geometry. Experimental data suggest that a and b fall
in the range 0.0 < a, b < 1.0
• Recommended Formula. Mean values for the onset of
instability can be established by fitting semi empirical
correlations to experimental data. The correlation form
chosen is
f n = natural frequencies of the
immersed tube
Vc = critical cross flow velocity

22.  For uniform cross flow, the tubes will be stable if the
representative cross flow velocity V is less than the critical
velocity V c .
The available 170 data points for onset of instability are
shown in Figure N-1331-4. In the range m(2πξn)/ρD2 > 0.7,
there are sufficient data to permit fitting of critical velocity
eq. to data for each array type.
The mean values of C are Conservative estimates of the mean
values of Vc/f nD for mt(2πξ n)/ρD2 < 0.7 can be obtained
using critical velocity eq. with a = 0.5 and the mean C given
in the table

23. Figure N-1331-4 Stability Diagram

24. Suggested Inputs
 Accurately predicting the critical velocity requires scale
model testing to determine the value of C and the damping
ratio in each application,
 Also, flow may pass around the edge of the bundle and
does not have the pure cross flow direction shown in Figure
N-1331-3, even within the bundle. Furthermore, when the
vibration amplitude is small, such as that experienced
during subcritical vibration, not all support plates are
active
 Damping ratios in this vibration mode are typically small,
from 0.1% in gas to about 1% in steam or water. When the
vibration amplitude is large, as characterized by the onset
of instability, support plate‐to tube interaction greatly
increases the damping ratio which can reach 5% or more.

25. Vibration damage patterns in HE
 Collision damage :
 Impact of tube against each other and against vessel wall
 Causes flattened tubes, boat shape spot at the mid span
of the tube
 Tube wall eventually wears thin and fails
 Baffle damage:
 Due to clearance between baffle hole and tubes OD and
presence of large fluid force, tube can impact the baffle
hole causing thinning of tube wall in circumferential u
even manner
 Continuous thinning eventually causes failure

26.  Tube sheet clamping effect:
 Tube may expand in tube sheet to minimize the crevice
between the outer tube wall and hole
 Due to this natural frequency of tube span is increased
 Stress is max at tube to tubesheet joint which could lead to
tube breakage
 Material defect propagation
 Flaws can propagate and cause failure
 Corrosion and erosion contribute to this phenomena
 Acoustic vibrations
 Acoustic resonance is due to gas column oscillations and is
excited by phased vortex shedding
 Heat exchanger shell and attached piling may vibrate
accompanied with large noise
 When acoustic resonance vibration approaches tube natural
frequency may lead to tube failure

27. Failure regions
 U-bends: Outer row have low natural freq and may fail
 Entry/exit areas: Impingement plates, large outer tube limits and
small nozzle diameter can contribute to restricted enter and exit
area creating high local velocities and producing damaging FIV
 Tubesheet region: Unsupported span of tube is longer adjacent to
tubesheet than those in baffle region resulting in lower natural
frequencies, this region also has entry and exit areas which result in
higher velocities. Both this factors contribute to failure
 Baffle region: Depending upon baffle spacing frequency of tubes
can vary large spacing can result in lower natural frequency and
more probability of failure
 Obstructions: Obstructions to flow such as tie rods, sealing strips
and impingement plates may cause high localized velocities which
can initiate vibrations in immediate vicinity

28. Factors affecting natural frequency
 Material properties
 Tube geometry
 Span shape
 Type of support at each end
 Axial loading on tube

29. Design considerations:
 Tube diameter: larger diameter increases MOI, thereby
effectively increasing the stiffness of the tube.
 Unsupported tube span: shorter the tube span greater is
the resistance to vibration. Multi segment baffles can be
used to reduce span length.
 Tube pitch: larger pitch to tube diameter ratio reduces cross
flow velocity.
 Entrance/ exit areas: impingement plates should be sized
and positioned so that area available for flow is not
restricted. Distribution belts can be used o lower velocity
by allowing shell side fluid to enter/exit the bundles at
several locations.

30. Design considerations:
 U-bend regions: optimum locations of adjacent baffles or
use of special bend support device
 Tubing material and thickness: high value of elastic
modulus in ferritic steels and ASS provide greater
resistance to vibrations. Tube metallurgy and wall
thickness also effects damping properties of the tube.
 Baffle thickness and tube hole size: increasing baffle
thickness and reducing tube to baffle hole clearance
increases the system damping.
 Omission of tubes: omission of tubes at predetermined
critical locations within the tube may be employed to
reduce vibration potential.

31. Structure of analysis (One way FSI)
Geometric
modeling
Meshing
(same for
both cases)
Transient
CFD analysis
CFD-structural
surface mapping
of pressure
Transient
structural
analysis
Post-
processing for
fatigue life
estimation
Meshing
(same mesh
with fluid
domain
suppressed)

32. THANK YOU