5.2 Thermowell Design and Wake Frequency

5.2 Thermowell Design and Wake Frequency

A thermowell is a pressure-boundary cantilever in a flowing fluid. It lets you replace a temperature sensor without opening the process, but it also sheds vortices. Topic 1.K asks you to connect geometry, velocity, density, natural frequency, and wake frequency well enough to decide whether a well is too long, too slender, or in need of a support (velocity) collar. ASME PTC 19.3 TW is the industry calculation framework that organizes those ideas. It is not on the NCEES list of design standards supplied with the 2027 PE Control Systems exam — treat the frequency-ratio limits as engineering practice you reason from, not as a code you search on exam day.

Type and dimensions

Three common shank types appear on datasheets and in wake-frequency models:

Dimensions the exam actually names:

• Insertion length U — unsupported length into the fluid (plus any lagging extension that still hangs free). This is the lever arm. First-mode natural frequency fn falls roughly as 1/U² for a cantilever.
• Tip diameter D — the diameter that sets the vortex scale. Wake frequency fs = St × V / D, so a fatter tip sheds slower.
• Bore — inside diameter for the sensor. A large bore with a skinny probe adds air gap (measurement lag) and can lower stiffness.
• Tip thickness — conduction path into the sensor. Thin tips are faster and weaker.

Immersion must still be long enough to kill stem conduction error (several well diameters in the fluid is a common field rule of thumb). That is the measurement-lag side of the tradeoff: a short, fat well is dynamically happy and thermally sluggish or biased toward the nozzle temperature.

Wake frequency, natural frequency, and the ratio

Flow past a bluff cylinder organizes into a von Kármán street. Vortices peel off at a Strouhal frequency

fs = St × V / D

St is order 0.2 for many process Reynolds numbers; on the exam use the correlation or value the problem (or handbook) gives. V is the fluid velocity at the well, not a pipe-average you forgot to area-correct if the stem asks for local velocity. Keep D and V in consistent length/time units so fs comes out in hertz.

The well's installed natural frequency fn comes from stiffness EI, mass per length, added fluid mass, and the unsupported length. Qualitatively:

• Longer U → much lower fn
• Larger root diameter or a taper → higher fn
• Heavier well material → lower fn from mass, while damping and Scruton number move the other way
• A velocity collar or other intermediate support shortens the unsupported span and raises support frequency / fn

The quantity you screen is the frequency ratio r = fs / fn.

• Transverse (lift) resonance sits near r ≈ 1. Industry practice after PTC 19.3 TW keeps r below about 0.8 so you stay out of the lock-in band below exact coincidence. Manufacturing tolerance, added mass, and the tendency of vortex shedding to lock onto the structure all eat that 20% margin.
• In-line (drag) resonance sits near r ≈ 0.5. Practice treats the band about 0.4 to 0.6 as a second danger zone when damping is low.

Passing "r < 0.8" is therefore not automatically a pass if you landed at r = 0.44 in a heavy liquid.

PTC 19.3 TW also checks steady drag stress, oscillating (fatigue) stress, and internal pressure. Frequency ratio is the gate most control-systems items emphasize; a well can pass frequency and still fail fatigue at the root fillet.

Scruton number and support frequency

Scruton number Sc is a dimensionless mass-damping parameter. It rises with the well's effective mass and structural damping and falls as fluid density ρ and D² rise. In words:

• High-density liquids → low Sc → in-line (0.4–0.6) motion is harder to ignore
• Low-density gases → high Sc → fluid damping can suppress in-line lock-in
• PTC 19.3 TW-style exceptions: if Sc ≥ 2.5 (and Reynolds number is not in a severe vortex regime), the in-line frequency-ratio restriction is often relaxed, while the r < 0.8 transverse screen usually remains. Extremely high Sc (order 64 in the same framework) can relax even that — rare in gas, essentially never a free pass in water.

Support frequency is the practical twin of fn: anything that shortens the free span (collar, shorter U, stiffer root) moves the well's first mode up. A collar does not change process velocity; it changes how much shank is allowed to sing.

You will not be asked to recite clause numbers from a standard that is not in the exam PDF. You will be asked whether raising velocity, density, or length makes the well better or worse, and whether a collar or a taper is the lever to pull.

Worked: velocity goes up, what has to change?

A tapered well has tip diameter D = 0.750 in = 0.0625 ft, Strouhal number St = 0.22, and installed fn = 120 Hz.

At V = 15.0 ft/s:

fs = 0.22 × 15.0 / 0.0625 = 52.8 Hz

r = 52.8 / 120 = 0.44 — already in the in-line band.

At a revamp velocity V = 25.0 ft/s (same D, St, fn):

fs = 0.22 × 25.0 / 0.0625 = 88.0 Hz

r = 88.0 / 120 = 0.73 — still under 0.8, but you have walked toward transverse lock-in, and you did not leave the in-line problem behind at the old rate.

fs scaled exactly with V. That is the first numeric lesson.

To put r back to 0.44 at 25 ft/s you need fn,new = 88.0 / 0.44 = 200 Hz. For a cantilever, fn ∝ 1/U², so

U_new / U_old = √(120 / 200) = 0.77

about a 23% shorter unsupported length — cut U, add a velocity collar, or both. A stiffer taper (more metal at the root) or a larger D also helps: larger D lowers fs and raises fn, which is why "go up a shank size" is a standard fix when there is room in the nozzle.

If measurement lag is already acceptable, do not lengthen the well to "get more average temperature." That is the fatigue-versus-lag tradeoff in the wrong direction. Lengthen only when stem conduction or stratification is the demonstrated problem and the frequency screen still passes — often with a collar so the newly unsupported tip span stays short. Helical strakes and similar vortex-suppression profiles are a specialty fix when you cannot shorten the well.

Failure modes

In-line fatigue at r ≈ 0.5 is not academic; it is why the modern frequency screen has two danger bands instead of only "stay away from 1.0." On the exam, name the mechanism (wake resonance, erosion, leakage) from the evidence, then pick the geometry change that raises fn or lowers fs without pretending PTC 19.3 TW is in the supplied standards list.