Thermowell
resonance.
Thermowells
are subject to more than just the static forces from the fluids going past. They
also can have vibrations induced from the fluid vortices in the wakes (the von
Karman wakes) created by the interaction between them and the fluids. This has
been known for a very long time and it is most significant in the realm of highly
energetic flows.The induced vibrations are very critical when their
frequency corresponds to the resonance frequency of a thermowell . Under such
conditions, the temperature sensors can literally be pounded to pieces. The thermowells
themselves can rupture in extreme cases. How is one to predict
these potentially serious conditions?
The information and resources below
can likely help. The basics of thermowells are covered in the relatively new
site page, "About Thermowells". The whole
subject of resonance effects was put into context for us shortly after its addition
to the website in 2002 Then we began an email exchange with a very interesting
engineer, David S. Bartran, Ph.D.,P.E.. It seems that he has spent the better
part of the last six years working on the problem. He sent along a simplified
version of some software that he developed and it was placed on a download section
of our Community Web site,
www.tempsensor.net where registered members could access it at no charge.
We made access a little obscure to keep away those without serious interest in
the subject. Below are some of Dr. Bartran's comments on the subject, gleaned
from the exchange and used with his permission, with a minimal amount of editing
to tie together the various aspects of the subject. The various emphases with
bold and italicised type face are added editiorially. Comments-DSB: BACKGROUND
In the course of thermowell analysis work, some engineering software
which is useful in predicting the application limits of thermowells and sensors
has been developed . The freeware version of that code that is restricted to steam
and condensate applications; basically a worse case evaluation scenario (available
at www.tempsensor.net
as download "Wellstress.exe"). The code is based on a finite
element analysis of the thermowell and its dynamic response to vortex shedding.
It also includes a thermal mode that permits an estimate of the thermowell error
and the response time constant. The calculation is quite sophisticated, but has
been used in countless studies where thermowell and/or sensor failures have actually
occurred. Most instrument engineers (including myself in the beginning)
are not prepared to comprehend such a complex analysis as part of the thermowell
selection process. The program basically performs a dynamic stress analysis of
the thermowell under flowing conditions. Most instrument engineers prefer to select
thermowells in the traditional manner. RUNNING THE FREEWARE CODE In
running the code, you'll notice that the thermowell error is often remarkably
low. Suggest that you try a low velocity case (steam 50#/300 F at 15000 lb/Hr
in a 16" line). The thermowell temperature sensor error becomes increasingly
significant at the lower flows. This is the result of radiation error. It
has been tested in Windows 95/98/ and 2000 systems and runs in a dos-like window. You
get past the "splash" screen by hitting return. It immediately starts
asking for data for the calculation. Only screen displays are offered. Press "e"
to exit or simply close the screen. None of the existing commercial thermowell
calculation software are quite so comprehensive nor have they been used to correctly
identify the root cause of actual thermowell failures, as this one has. CONCERN
ABOUT MISAPPLICATION OF THERMOWELLS, SAFETY & PROCESS IMPLICATIONS The
simplified program provided has as its primary purpose to generate an interest
in a rational approach to thermowell selection and to temperature measurement
generally. This code, with more complete fluid calculations, has been
used to carry out dozens of post mortem analyses of failures. These failures are
for the most part taken from the published literature and some personal experience.
The combined total of documented failures currently exceeds ~50 applications.
One of the problems is that most thermowell failures are not properly identified.
For example, there are no inspection procedures or testing protocols established
in the standards organizations or within the proprietary arena. I am afraid
that most failures are treated on a replacement basis and rarely cause for a safety
report. However, the few that have been are clearly explained when the dynamic
analysis used in this code has been used. Of concern, is that 30%
of thermowells are mis-applied when taken across all process applications. While
this number sounds high, it has been independently confirmed by other researchers
(oil field production). That said, failed thermowells are capable of
causing a surprising amount of damage inside the process and in the immediate,
external area. Personnel risk is also an issue. Sensor reliability
is also an issue, with sensor stresses frequently exceeding 250 G's in high velocity
liquid and compressible flow services. Once the tip acceleration (vibratory) exceeds
5-10 G's, the sensor will literally "jack-hammer" itself to pieces even
with spring-loading. The method for the stress calculation and the
basis for setting the maximum allowable stresses are covered in the following
articles: Flow
induced vibration of thermowells, ISA Trans. 38, 1999 Static
and dynamic stresses of practical thermowells, ISA Trans., 39, 2000 Thermowell
design and selection, Hydrocarbon Proc., Nov. 2001. Are
your thermowells safe?, TAPPI (Pulp & Paper) Journal, April 2002. Thermowell
integrity in pipeline services, Oil & Gas Journal, April 2002. MORE
ABOUT THE SOFTWARE The thermowell analysis has been applied to finned
thermowells (quite interesting from a stress and measurement error perspective),
refractory lined furnaces (extremely complex), and other more common applications.
You'll also notice that if you press "r" when the splash screen is up
you get the references used to define the basis of the calculation. Of course
those aren't the only papers in the literature, but they are the ones that describe
the calculation. Interested parties can get copies from the journals and
magazines involved. It would be great to have permission to put the papers on
this web-site, but that could be a cost issue from the respective publisher. (ED
NOTE: We are looking into it) GOING BEYOND THE SIMPLE VERSION If
someone has specific runs in mind about specific applications, I can run the calcs
(gratis) and send them to you until we see what the need is. (ED Note: Please
send any inquires to us at twell@temperatures.com with as much detail as possible,
so we can pass them along ) The code is still engineering software for
the arbitrary application, but it is well behaved (and tested) for the steam and
condensate applications that one encounters in industry. I am hesitant to put
it in arbitrary hands at this point. Steam is a well defined application in most
plants, that is easily justified. MORE THAN A SIMPLE DEMO Here
is a site specific code with a few more bells and whistles than the version given
out as a means for generating awareness about a rational approach to thermowell
selection. (Members only download from www.tempsensor.net
as WellStress2.exe) Additional features included: Uses
3 modes in the modal analysis, includes variable pipe wall (carbon steel assumed)
and insulation thickness (representative insulation k values used). It is otherwise
identical with the original demo code. Also included is the specification of the
tip thickness of the thermowell design. As a design practice the minimum tip thickness
should be greater than the bore diameter. The code uses a finite element
model of the thermowell to develop the critical frequencies and mode shapes for
the three basic thermowell designs (straight, stepped and tapered designs). The
drag stresses (due to bending in the flow direction) are developed by piecewise
integration of the fluid force distributed along the thermowell. A uniform flow
profile is assumed. Once the dynamic modes of the thermowell are
determined, it is a simple matter to construct the stress response to a combination
of drag and vortex shedding forces. Modal superposition is used. A simplified
force model of the vortex shedding process is used. It includes both in-line and
transverse force components. The in-line force oscillates at twice the frequency
of the vortex shedding rate and has been demonstrated to produce damaging levels
of stress in both liquids and high pressure gases and vapors. The drag coefficient
and the transverse lift coefficient are taken as unity to insure a conservative
estimate. The in-line oscillating drag is assigned a value equal to 10% of the
transverse lift coefficient. The Strouhal is taken as constant ~0.22. It
is not necessary to invoke Reynold's number dependencies since the in-line vortex
shedding force have been explicitly included. STRESSES and TEMPERATURE
CALCULATIONS As a basis for design, the tip stress and the hydrostatic
"hoop" stress should always be less than the maximum allowable stress,
as defined in the appropriate piping code (B31.1 or B31.3 according to the specification
of the adjacent piping). The dynamic bending stresses are a bit more complex
and are not uniformly distributed. For the purposes of design, the peak
stress is taken as the sum of the peak in-line and the peak transverse stress
at a given velocity. This combined stress should be less than 50% of the maximum
allowable stress as defined in the piping codes. The 50% derating is used to account
for the fact that the oscillatory stress components involve stress reversals and
reduce service life. A greater level of derating should be appied in corrosive
services. Other definitions can be used, but this approach produces evaluations
that correctly identify high risk design/applications in case studies of documented
failures. Unlike most thermowell stress calculations the damped response
of the thermowell is permitted. This insures that stress estimates can be made
when the vortex shedding process excites the thermowell to resonance either as
a result of in-line or transverse resonance. The damping coefficient is representative
of test performed with actual thermowells. It can be greater or smaller in specific
instances and depending somewhat on the flexibility of the thermowell installation,
so a mean value of 0.31% is used. Thermowell temperature error is calculated
by direct integration. Conductivity, convection and nominal radiation terms are
included in the thermal model. The convection coefficient is taken from Incropera
and DeWitt (Reference 1). It is conservative and is well suited for thermowell
applications. The temperature at the pipe wall is taken as the boundary
condition for the thermowell. This is somewhat arbitrary, but it provides a useful
approximation to the actual condition. The temperature profile (a thermowell error)
is developed interatively until thermal equilibrium is achieved at the tip. Thermowell
error is largely driven by the "wall deficit", that is the difference
between the temperature on the inside pipe wall and the flowing fluid temperature.
It is controlled by the amount of heat loss from the pipe wall and the thermowell
connection. It is the driving force behind most of the thermowell portion of the
measurement error. Contrary to traditional practice, thermowell length plays
a secondary role in thermowell error. High wall deficits are associated with an
increasing radiation error component. This can be seen in low pressure steam in
cases where the pipe is un-insulated and the steam velocity is low. It shows up
as what appears to be a flow independent offset in the measurement error. The
"longer is better" rule of thermowell selection has been an article
of faith in thermowell selection since day one. This was a requirement for filled
system devices, but is no longer valid for modern thermocouple and RTD sensors.
As long as the thermowell tip is exposed to the process and is greater than two
diameters in length, conduction errors are insignificant as long as the pipe is
well insulated. The properties of steam and condensate are taken from the
equation of state documented in Keenan and Keyes (Reference 2). If the pressure
and temperature specified are incompatible with the physical state of the fluid,
then the properties are calculated at saturated conditions. KEY TO THERMOWELL
SELECTION The key to proper thermowell selection is avoidance of high
risk designs over the range of flows that you expect to encounter. All high velocity
resonances should be avoided, not only because of the risk of thermowell failure,
but also because of the vibratory stresses (tip acceleration stresses) can literally
pound delicate sensors into oblivion. At resonance, the tip acceleration stresses
can easily exceed 250 G's. These stresses have been measured by several investigators.
Most spring loaded assemblies are only rated for 5 G's, with some proprietary
designs rated to 25 G's. Clearly, few sensors (specifically platinum rtd's) can
sustain vibration stresses without decalibration due to work hardening. Thermocouples
appear to be less prone to vibratory damage. A
CLEARINGHOUSE FOR THERMOWELL/SENSOR PROBLEMS?
There is a crying
need for a clearing house for the exchange and sharing of thermowell/sensor problems
that goes beyond what the ASME, ISA, API, etc. are able to provide. (ED NOTE:
Contact us at twell@temperatures.com,
if you are interested in being involved in a discussion forum on thermowell/sensor
problems). References:
1.
Introduction to Heat Transfer, 3rd Edition, Frank P. Incropera, David P.
DeWitt, John Wiley & Sons, Inc. New York (1996)
2. Steam Tables
: Thermodynamic Properties of Water Including Vapor, Liquid, and Solid Phases/With
Charts (metric measurements), Joseph H. Keenan, Frederick G. Keyes, Philip
Gl Hill, Joan G. Moore, John Wiley & Sons, Inc. New York (1992)
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