Temperature · 3.6

Thermowell wake frequency: why a well can pass every stress check and still fail

25 October 2026 · 11 min read · ASME PTC 19.3 TW

In short

Vortices shed from a thermowell at f_s ≈ 0.22 V / B. If that comes near the well's natural frequency, the well resonates and fails by fatigue.
There are two resonances. The in-line one, at about half the natural frequency, arrives at half the velocity and is the one older methods missed.
Keep f_s / f_nc at or below 0.4, unless the standard's exceptions apply.
Natural frequency falls with the square of the length, so shortening the well is almost always the fix.

A thermowell is a cantilever sitting in a moving fluid. As the fluid flows past, vortices peel off the well, first from one side and then the other, and every vortex gives the well a small push. If that pushing frequency comes near the well's own natural frequency, the well resonates. A few hours of resonance can crack it at the root, and the broken tip goes downstream.

This is a fatigue failure, not an overload. The steady stress can be tiny and the well can still break. That is why ASME PTC 19.3 TW puts a frequency limit next to the stress checks, and why the frequency limit is the check that usually sets the immersion length.

Where this matters

The risk is highest where velocity is high and the well is long: gas and steam lines, compressor discharges, high-velocity liquid lines and any well sitting in a reduced bore. Low-velocity liquid service rarely governs. A broken well is a loss of containment at the root, and the broken tip can damage downstream equipment such as meters, valves or a compressor.

Thermowell failures of this kind are not rare. The best known is the sodium leak at Japan's Monju fast-breeder reactor in 1995, which started at a thermowell broken by flow-induced vibration. In process plants the usual story is less dramatic: a well that was fine on water is reused, unchanged, on a gas or steam line.

How it works

The two frequencies

The shedding frequency, f_s

Vortices leave the well at a rate set by the velocity and the diameter near the tip:

f_s = N_s × V / B

V is the fluid velocity, B is the tip diameter and N_s is the Strouhal number, about 0.22 over most practical Reynolds numbers. (The standard gives N_s as a function of Reynolds number. 0.22 is a fair working value, so use the full curve in the final check.) So f_s doubles when the velocity doubles and rises as the tip gets thinner.

The well's natural frequency, f_nc

The starting point is the textbook first mode of a uniform cantilever:

f_a = (1.875² / 2π) × √(E·I / m) / L²

E is the elastic modulus at temperature, I is the second moment of area, m is the mass per unit length and L is the unsupported length. PTC 19.3 TW then applies correction factors. One accounts for the taper, which stiffens the well and raises the frequency. Two account for the added mass of the fluid and of the sensor, which lower it. A further one, the support compliance H_c, allows for the fact that a flange or a nozzle is never perfectly rigid. H_c typically takes off 5–15 %, and leaving it out was one of the reasons the old method was unsafe.

Note the L². The natural frequency falls with the square of the length. Making a well 20 % longer cuts its natural frequency by about a third. This is why the fix is almost always "shorten the well", and why a long well on a fast gas line is the classic failure.

The two resonances, not one

The vortices push the well in two directions:

Transverse (across the flow), once per vortex pair, at f_s. The well resonates when f_s ≈ f_nc.
In-line (along the flow), once per vortex, at 2 f_s. The well resonates when 2 f_s ≈ f_nc, that is f_s ≈ 0.5 f_nc.

The in-line force is smaller, but the in-line resonance arrives at half the velocity. The old method (PTC 19.3-1974, based on Murdock's 1959 work) only kept clear of the transverse resonance. The 2010 rewrite, PTC 19.3 TW, added the in-line resonance, and many wells that passed the old rule fail the new one.

What the standard says

With r = f_s / f_nc, the frequency ratio, the frequency limit works like this:

Frequency ratio r	Result
r ≤ 0.4	Acceptable. The well is below the in-line resonance.
0.4 < r < 0.6	In the in-line lock-in band. Not acceptable, unless the in-line resonance is suppressed (see below).
0.6 ≤ r < 0.8	Acceptable only if the stress while passing through the in-line resonance on the way up is within the fatigue limit. The flow has to cross r = 0.5 at every start-up.
r ≥ 0.8	At or near the transverse resonance. Not acceptable under the normal criteria.

When the in-line resonance is suppressed: a dense, well-damped well in a light fluid, with Scruton number N_Sc above 2.5 and Reynolds number below 10⁵, does not lock in-line. Then r < 0.8 is enough. This mostly helps on low-pressure gas, and rarely on liquids.

When the check is not needed: if the velocity is below 0.64 m/s (2.1 ft/s) and the well meets the standard's minimum dimensions and material strength, the frequency limit can be skipped.

Worked example: a natural gas line

Here is a common case, a tapered flanged well on a gas header:

Input	Value
Fluid	Natural gas, 40 barg, 40 °C, ρ = 32 kg/m³, µ = 0.012 cP
Velocity	20 m/s
Well	316 stainless, tapered, root A = 27 mm, tip B = 19 mm, bore d = 6.6 mm, one-piece (not welded)
Material at 40 °C	E ≈ 194 GPa, ρ = 8000 kg/m³

Shedding frequency. f_s = 0.22 × 20 / 0.019 = 232 Hz. This does not depend on the length.

Reynolds and Scruton numbers. Re = ρVB/µ ≈ 1.0 × 10⁶ and N_Sc ≈ 1.1, so the in-line resonance is not suppressed and the 0.4 / 0.6–0.8 rule applies.

Now three lengths, from a specification that asked for "250 mm standard":

Unsupported length L	f_nc	r = f_s/f_nc	Frequency limit
250 mm	335 Hz	0.69	Fails. Passing through the in-line resonance gives ≈ 260 MPa against a 94 MPa fatigue limit.
200 mm	513 Hz	0.45	Fails. Sits in the in-line lock-in band.
150 mm	879 Hz	0.26	Passes, below 0.4.

Two things in this table are worth noting.

The 250 mm well's dynamic stress at 20 m/s is only about 10 MPa. Judged on the operating point alone it looks comfortable. It fails because the flow has to pass through r = 0.5 every time the line comes up to rate, and at that moment the well is in resonance. A stress check at normal flow alone would have missed this.
Shortening from 250 to 150 mm raised f_nc by a factor of 2.6. That is the L² effect, plus a small gain in the support factor H_c.

The fatigue limit used here is the class A endurance limit of PTC 19.3 TW-2010 for a well with no welds, 93.8 MPa. A welded well (for example, a well welded to its flange) has a much lower limit, 21 MPa, so the 0.6–0.8 window is almost never usable for welded wells.

When it fails: the fixes in order

Shorten it. This is the most effective fix. Check that the sensing element is still in the flowing stream. For most services, a tip in the middle third of the pipe is enough for a representative reading.
Make it stiffer. A larger root diameter raises f_nc. A thicker tip helps less, because a larger B also lowers f_s, but it reduces stress.
Move it. A larger line or a lower-velocity location (an elbow-mounted well pointing into the flow, or a bigger branch) reduces V.
Be careful with velocity collars and helical strakes. Collars depend on a tight fit in the nozzle that is hard to guarantee and that changes over time. Strake designs fall outside the standard's method and need the vendor's test data. Neither is a substitute for getting the length right.

Common mistakes

Checking only normal flow, and missing the start-up pass through the in-line resonance.
Using the header average velocity instead of the velocity at the well's own bore.
Applying the 1974 (Murdock) method, which ignores the in-line resonance and the support compliance.
Reusing a "standard" 250 mm well from a water line on a gas or steam line.
Using room-temperature properties for a hot service.
Ignoring whether the well is welded, which changes the fatigue limit by a factor of more than four.

Checklist

Run the calculation at minimum, normal and maximum flow, and think about start-up, blowdown and gas lift cases. The highest velocity is not always the worst. A ratio sitting near 0.5 at a low flow can be the governing case.
Use the velocity at the well's location, from the actual line bore, not a header average.
Use E and the allowable stress at operating temperature.
Record the well's actual dimensions (A, B, d, L and the tip thickness) from the vendor drawing, not a catalogue "standard" well.
State whether the well is welded or one-piece, because it changes the fatigue limit by a factor of more than four.
Remember that the frequency limit is one of four checks. The others are steady stress, dynamic stress and pressure rating of the shank and tip. A well must pass all four.
Re-run the check whenever the flow, fluid or line size changes. A well moved from a water line to a gas line is a new design.

Quick reference

Shedding frequency: f_s = N_s V / B, with N_s ≈ 0.22
Natural frequency: f_a = (1.875² / 2π) √(EI / m) / L², then corrected for taper, added mass and support compliance to give f_nc
Accept: r = f_s / f_nc ≤ 0.4. 0.4 to 0.6 is not accepted. 0.6 to 0.8 is accepted only if the in-line passage stress passes. 0.8 and above is not accepted.
In-line resonance suppressed when N_Sc > 2.5 and Re < 10⁵. Then r < 0.8 is enough.
Frequency check not needed below 0.64 m/s (2.1 ft/s), if the minimum dimensions are met.
Fatigue limit (class A, TW-2010): 93.8 MPa one-piece, 21 MPa welded.