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# Thermowell Wake Frequency Calculation & Theory

Thermowell wakes, and the resulting thermowell wake frequency, is a physical characteristic resulting from the interaction of a thermowell with the fluid flowing past it. The thermowell dimensions and geometry, and the properties and process conditions of the fluid flowing past the thermowell all determine the effects and frequency of the wake vortices. In some applications, the wake frequency can result in the design of the thermowell being unsuitable for the application, and use of such a thermowell being a potential safety hazard.

## Thermowell Wake Frequency Theory

In a pipeline, a thermowell extends into a flowing fluid which exerts forces upon the stem of the thermowell. Static forces are exerted by the mass of the fluid impacting on the thermowell. Additionally, as the fluid flows past the thermowell, the change in fluid momentum creates a turbulent wake behind the well. Vortices, known as "Von Karman vortices", form in this wake and shed from alternate sides of the well. The vortex shedding frequency (or wake frequency) is linear with fluid flow velocity and inversely proportional to thermowell tip diameter.

## Why is Thermowell Wake Frequency a Concern?

The vortex induced forces cause the thermowell to vibrate. The magnitude of these thermowell vibrations are generally negligible. However, as the wake frequency approaches the natural frequency of the thermowell the vibrating forces increase, and when the wake frequency matches the natural frquency of the thermowell it goes into resonance. At resonance the vibrating forces increase rapidly, and the resultant vibrations can cause thermowell failure.

If the thermowell stem shears then it could travel at high velocity down the pipeline causing damage to downstream equipment e.g. pumps, valves etc. Additionally, the temperature measurment instrument within the thermowell (e.g. thermocouple or RTD) is now exposed to pipeline presure. This could cause the measurement instrument to be pushed out of the thermowell head leading to a loss of pipeline fluid containment.

It is therefore vital that the instrument engineer considers wake frequency when performing thermowell sizing and thermowell specification.

## Thermowell Wake Frequency Calculations

Thermowell wake frequency calculations should be conducted during thermowell specification and definately prior to thermowell manufacture. These thermowell calculations ensure that the thermowell design is robust enough to cope with the forces produced by the process media.

It is not strictly necessary to carry out a wake frequency calculation for every thermowell. Many instrument engineers only carry out wake frequency calculations when the fluid flow rate is high (typically in gas flows) and the damping effect of the fluid is low, or when the thermowell insertion length is long compared to the pipe internal diameter.

Reputable suppliers of thermowells are only too happy to provide an individual calculation of the stresses induced upon and the relative strength of their thermowells - this provides a useful check on any calculations you may perform.

## Standards for Thermowell Wake Frequency Calculations

**ASME PTC19.3-1974**, and the later **ASME PTC19.3TW-2010** have been the standards used for many years to design most thermowells.

**ASME PTC19.3TW-2016** is a newer standard, released in 2016 to replace the 2010 standard. It uses more advanced methods for evaluating the suitability of a thermowell for a specific application, and is applicable to tapered, straight and reduced-tip profiles. It is not applicable for fabricated (welded tube) thermowells.

It references work carried out by Murdock, which is now the accepted standard for harmonic frequency analysis of thermowells. Given the calculated harmonic frequency of the thermowell stem, the standard provides a method of calculating the induced frequency from the vortices. The standard then requires a safety margin to be applied such that the induced frequency is no more than 80% of the thermowell harmonic frequency.

## Thermowell Wake Frequency Spreadsheet & Online Calculator

Budenberg, who make themowells in the UK provide an MS Excel spreadsheet with thermowell wake frequency calculations based on ASME PTC19.3TW-2010. This spreadsheet should be used as a guide only - it lets you, the instrument engineer determine whether further detailed calculations need to be performed on the thermowell you are specifying.

Click on the following link to open the spreadsheet ASME PTC19.3TW-2010 Wake Frequency Calculation

Emerson, the multinational instrument supplier provide an online thermowell wake frequency calculator based on ASME PTC 19.3TW-2016. This online calculator is intended to be an aide in selecting a thermowell, and will indicate if further more detailed calculations are required.

Click on the following link to open the online calculator ASME PTC19.3TW-2016 Wake Frequency Calculation

## Changing Thermowell Design to Alter Frequency Ratio

If the calculated wake frequency is too close to the natural frequency of the thermowell i.e. the ratio is greater than 0.8, the following structural changes to the design of the well may be a solution:

Change the thermowell dimensions and/or geometry, this will also changes the resonant frequency. Things to consider include:

### Shorten the Insertion Length

Shortening the thermowell insertion length is the most effective method, and the recommended method from ASME PTC 19.3 TW-2016, for the improvement of the frequency ratio.

### Increase the Root Diameter

By increasing the root diameter of the thermowell, the natural frequency is increased and the frequency ratio improved.

### Increase the Tip Diameter

By increasing the tip diameter of a thermowell, the vortex shedding frequency is reduced. Again, this leads to an improvement in frequency ratio.

### Use a Velocity Collar

The use of velocity collars (also known as support collars) is not generally recommended. ASME PTC 19.3 TW-2016 points 6-7-(e) points out that rigid support can be obtained only with an interference fit between the velocity collar and the installed piping, and anyone who has tried to install a thermowell with support collar will know that obtaining an interference fit can sometimes be tricky. In fact velocity collars or other means of support are outside the scope of the ASME PTC 19.3 TW-2016 standard.

Despite the above many manufacturers will, on customer request, provide thermowells with support collars. In this case the thermowell will be designed in accordance with the design and calculation criteria of ASME PTC 19.3 TW-2016, but crucially will fall outside the scope of ASME PTC 19.3 TW-2016 and a guarantee for support collar solutions is generally not given.

When a support collar solution is provided the operator is responsible for ensuring the rigid support of the collar in the nozzle, which may mean that a reworking of the collar is needed.

### Provide a Helical Vane

A helical vane, or more correctly a strake, on the stem of the thermowell deliberately introduces turbulence resulting in the resonant load frequencies having negligible amplitudes. The effectiveness of helical strakes for reducing vortex induced vibrations was discovered by Christopher Scruton so these vanes are often described as Scruton strakes. For maximum effectiveness in suppression of vortices caused by gas flow, each vane or strake should have a height of about 10 percent of the cylinder diameter, and its length should be approximately 5 times the cylinder diameter.

Thermowell's with a Scruton strake are a bespoke solution and are generlly only provided by the major thermowell suppliers e.g. Wika produce and market a thermowell with Scruton strakes called the "ScrutonWell®".

## Technical Library

The following pages give more detail on the techniques used in temperature measurement:

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For those who want to read further about the theory and practice of measuring temperature, and broaden their understanding of the differing types of temperature instrumentation, then the following books from Amazon will be of interest: