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Thermowell Wakes, Vortices, Vibrations & More


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.



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.


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.


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.


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)


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.


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.


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.


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.


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).


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)

Tell your new product and application stories at The Temperature Community website: www.tempsensor.net or feedback to us and we'll consider adding it here with your byline!

Good luck and best wishes. If you have some interesting successes, let us know and we'll help you share that with others who visit these pages.

Here are some useful technical links relating to thermowell design and applications. A seperate vendor's page is available listing some of the many makers of thermowells around the world.

  • Enercorp's
    Thermowell comments: thermowells will reduce the possibility of damage to the temperature sensor from corrosion, pressure or the flow of abrasive or viscous media.
  • Corrosive Service Guide
    Thermowell Corrosive Service Guide from Tempco Electric-Includes Hydrobromic Acid, Hastalloy C etc.
  • A forum about Thermowells
    Discussions to share thermowell calculations by a software vendor.
  • Thermowell Materials
  • Thermowell Resonance.
    Thermowells have been known to fail due to induced vibrations from the flow of gases going past it-(another view on the subject)

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