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### Thermowell Vibration Excel Calculator

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**Fluids Engineering and Design**

Thermowell Vibration Fluids Engineering Systems Excel Calculator Spreadsheet

These calculations are performed according to the paper "Power Test Code Thermometer Wells" by J. W. Murdock, and also meet the requirements of ASME PTC 19.3-1998. The program supplies results which should only be used as a guide for thermowell design.

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When fluid flows past a thermowell, the change in fluid momentum creates a turbulent wake behind the well. Vortices form in this wake, and shed from alternate sides of the well. The vortex shedding frequency (or Wake frequency) is linear with flow velocity and inversely proportional to thermowell tip diameter.

These shedding vortices impose on the thermowell, a periodic force comprising two components – (i) a lift force, normal to direction of flow, oscillating at the wake frequency, and (ii) a smaller drag force, parallel to flow, oscillating at twice the wake frequency.

These vortex-induced forces, which cause thermowell vibration, are normally small with the magnitude of the vibrations generally negligible. However, as the wake frequency (fw) approaches the natural frequency (fn) of the thermowell (within 20%), it can shift and lock-in to the natural frequency. When fw = fn, the thermowell goes into resonance, and vibrating forces increase rapidly. The resultant vibrations can cause mechanical failure of the well.

The Murdock calculations (and companion ASME PTC 19.3) consider only the oscillating lift force as the cause of thermowell vibration. The ratio of wake to natural frequency is restricted to a maximum of 0.8 to eliminate the possibility of resonance.

Although the oscillating drag force is small, it can force the thermowell into resonance at lower velocities because it occurs at twice the wake frequency. For high-density fluids (liquids and high pressure steam), the Murdock analysis is not adequate. When the oscillating drag component is included, the velocity rating can be reduced by up to 50%.

The calculations included herein are modified to include in-line resonance due to the oscillating drag force, correction for the magnification ratio and use of the actual natural frequency of the well rather than the estimated value.

The results of these calculations shuld only be used as a guide in the selection of the correct thermowell. Other variables, like corrosion, should be evaluated and influence the decision.

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