Thermowell Wake Frequency Calculator
This calculator validates the mechanical stability of thermowells against flow-induced vibrations, specifically addressing vortex-induced resonance. It adheres to the guidelines of ASME PTC 19.3 TW-2016 and is essential for ensuring the integrity and safety of thermowells in industrial processes worldwide.
Calculation Results
Thermowell Diagram (Simplified)
Stability Status: N/A
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Professional Insights: Thermowell Failure Explained
What is a Thermowell?
A thermowell is a strong, sealed tube that protects a temperature sensor (like a thermocouple, RTD, or thermometer) from the process fluid it's measuring. Think of it as a permanent "sleeve" installed in a pipe or vessel. This allows the sensor to be safely removed for calibration or replacement without shutting down or draining the entire process.
While it provides essential protection, the thermowell itself, being a blunt object protruding into a moving fluid, is subject to powerful aerodynamic (or hydrodynamic) forces. Failure to properly engineer this component can lead to catastrophic mechanical failure.
The Danger: Flow-Induced Vibration (FIV)
When a fluid (like steam, gas, or liquid) flows past a thermowell, it doesn't just flow *around* it; it creates a turbulent pattern called a Kármán vortex street. The fluid creates swirling vortices, or "wakes," that detach from alternating sides of the thermowell. You can see this same effect when wind blows past a flagpole, causing it to "sing" or flutter.
This alternating vortex shedding creates a periodic force that pushes the thermowell back and forth, perpendicular to the direction of the flow. The frequency of this pushing force is called the wake frequency (fw).
Resonance: The "Silent Killer"
Like a guitar string, every physical object has a natural frequency (fn)—the frequency at which it "wants" to vibrate if you "pluck" it. This is determined by its length, diameter, material stiffness (Young's Modulus), and how it's mounted (e.g., cantilevered).
Resonance is the catastrophic phenomenon that occurs when the external forcing frequency (the wake frequency, $f_w$) gets too close to the thermowell's internal natural frequency ($f_n$).
When this "lock-in" occurs, the tiny pushes from the vortices perfectly align with the thermowell's own vibration, amplifying the motion with each cycle. The vibrations can grow exponentially, leading to high-cycle fatigue and causing the thermowell to snap off and be sent downstream, potentially destroying pumps, turbines, or other critical equipment.
The goal of this calculation, and the entire ASME PTC 19.3 TW-2016 standard, is to ensure this never happens.
The ASME PTC 19.3 TW-2016 Standard
This is the global standard for the mechanical design and selection of thermowells. It is a rigorous check that evaluates multiple failure modes. This calculator performs the most critical of these checks: the frequency limit.
The standard mandates several checks, including:
- Frequency Limit (This Calculator): The primary safety check. The standard states that the thermowell's natural frequency ($f_n$) must be high enough to avoid resonance. The wake frequency ($f_w$) must be less than 80% of the natural frequency.
$f_w < 0.8 \times f_n$ (or) $\frac{f_n}{f_w} > 1.25$
- Static Stress Limit: Checks if the thermowell is strong enough to resist the simple "push" (drag force) of the fluid without bending or breaking.
- Dynamic Stress Limit: Checks if the thermowell can withstand the cyclic stress from the vibrating forces, even if it's not in full resonance.
- Pressure Rating: Ensures the thermowell can withstand the process pressure without bursting.
Note: This tool only evaluates the Frequency Limit. A complete design must satisfy all four criteria.
How to "Fix" a Failing Thermowell Design
If the calculation shows a failure ($f_n / f_w < 1.25$), the design is unsafe and must be changed. Engineers have several options, all of which aim to either increase the natural frequency ($f_n$) or disrupt the wake frequency ($f_w$):
- Shorten the Insertion Length (L): This is the most effective solution. $f_n$ is inversely proportional to $L^2$. Halving the length quadruples the natural frequency. This is why you should always use the shortest thermowell possible that still reaches the representative flow.
- Increase the Root/Tip Diameter (D): A thicker thermowell is stiffer, which increases $f_n$. A larger diameter may also reduce the wake frequency ($f_w = S_t \times U / D$).
- Change Material: Using a stiffer material (higher Young's Modulus, $E$) or a lighter material (lower $\rho_s$) will increase $f_n$.
- Add a Velocity Collar: This is a support collar added partway down the thermowell. It effectively "shortens" the unsupported length ($L$) and changes the mounting from a simple cantilever, dramatically increasing $f_n$.
- Use a Helical Strake Profile: Instead of a smooth cylinder, these thermowells have a helical (spiral) fin. This design, borrowed from industrial chimneys, "trips" the fluid flow and breaks up the vortices, preventing a coherent, resonant wake from ever forming. This *disrupts* $f_w$ rather than changing $f_n$.
Key Parameters in the Calculation
- Reynolds Number ($R_e$): A dimensionless number that describes the flow regime (laminar, turbulent). It's calculated using fluid density, velocity, diameter, and viscosity. $R_e$ is used to find the correct Strouhal number.
- Strouhal Number ($S_t$): A dimensionless number that links the wake frequency, velocity, and diameter. For most industrial flows ($R_e > 1000$), $S_t$ is a near-constant, typically around 0.22.
- Young's Modulus ($E$): A measure of material stiffness. A higher $E$ (like Hastelloy) means a stiffer thermowell and a higher $f_n$ compared to a more flexible material (like Titanium). This value also decreases as temperature increases.