Thermowell Wake Frequency Calculation: 6-Step Field Guide
A thermowell wake frequency calculation prevents structural failure from vortex shedding by proving the vortex frequency stays safely below the well’s natural frequency, usually under 80 % of it, per ASME PTC 19.3 TW-2016. This guide walks through the six steps we use on real refinery and power-station projects, with a worked example, the GB/T 30121-2013 equivalent for China sites, and the three ways to fix a thermowell that fails the calc.
What Wake Frequency Is, in 60 Seconds
When steam, gas, or liquid flows past a cylindrical thermowell, alternating low-pressure vortices shed off each side. This is the Kármán vortex street. Each shed vortex tugs the thermowell sideways at the wake frequency, fw. Every thermowell also has a natural frequency, fn, set by its length, root diameter, material stiffness, and end fixation. When fw climbs close to fn, the tugs resonate with the well’s vibration mode and amplify. Failures happen in hours, not years.
ASME PTC 19.3 TW-2016 caps the frequency ratio fw/fn at 0.8 for steady-state service and 0.4 for in-line resonance; the second limit is the one engineers miss most often. The standard also requires three other checks: cyclic stress, steady-state stress, and pressure rating. A thermowell must pass all four.
The Four Checks Hidden Inside “Wake Frequency Calculation”
Most engineers say “wake frequency calc” but really mean the full PTC 19.3 TW-2016 evaluation. The standard runs four interlocking checks:
| # | Check | What it bounds | Typical failure mode |
|---|---|---|---|
| 1 | Frequency ratio (fw/fn) | < 0.8 transverse, < 0.4 in-line | Resonance, fatigue at the root |
| 2 | Oscillating bending stress | < material fatigue limit | Cyclic crack growth |
| 3 | Steady-state stress (drag + pressure) | < allowable per ASME B31.x | Plastic deformation |
| 4 | Pressure rating | < TW rating at temperature | Burst |
A thermowell that passes frequency but fails oscillating stress is just as dead. We have seen exactly that on a turbo-expander discharge line where U was shortened to clear frequency but the tip got thin enough that cyclic bending stress went over.
How to Calculate Thermowell Wake Frequency: 6-Step Procedure
This is the sequence we run on every new spec sheet that crosses our desk:
- Collect the five process inputs. Velocity (m/s or ft/s), density (kg/m³), dynamic viscosity (Pa·s), maximum pressure, maximum temperature. Without all five, stop and ask the process group for the missing one.
- Compute Reynolds number, then read Strouhal. Re = ρ·V·d / μ where d is the thermowell tip diameter. For most industrial flows (Re between 1,000 and 5 × 10⁵) the Strouhal number St sits near 0.22, but PTC 19.3 TW-2016 uses a variable St that depends on Re. Use the table in the standard, not 0.22 blindly.
- Compute wake frequency. fw = St · V / d. Velocity in m/s, d in meters, fw comes out in Hz.
- Compute natural frequency. fn = (K · d_root / L²) · √(E / ρ_material), where K is a fixation factor (0.560 for clamped-free per PTC 19.3), d_root is the root diameter, L is the unsupported length, E is the modulus of elasticity, and ρ_material is the material density. Use the corrected formula in the 2016 revision; earlier editions overpredict fn by 5 to 15 %.
- Compute the ratio. fw / fn. If less than 0.8, transverse resonance is cleared. Then re-run fw / fn against 0.4 for the in-line check. This is the catch most online calculators forget.
- Run the remaining three checks. Oscillating bending stress at the root, steady-state combined stress, and pressure rating against the maximum temperature class. All four must clear before the spec sheet ships.
Quick Wake-Frequency Calculator (PTC 19.3 TW-2016 first-pass)
Plug in your line spec; verify with the official Ashcroft or WIKA tool before issuing the spec sheet.
First-pass sizing only. The PTC 19.3 TW-2016 oscillating- and steady-stress checks are not included; use the official Ashcroft, WIKA, or Pyromation calculator before issuing a spec sheet.
The Chinese national standard GB/T 30121-2013 (Industrial-platinum and copper resistance thermowells — protection tubes) covers the same calculation framework with slightly different scope. The parameter map below is the cheat-sheet we hand to bilingual EPC teams: symbol on the left, identical physical meaning across both standards.
| Symbol | ASME PTC 19.3 TW-2016 term | GB/T 30121-2013 term |
|---|---|---|
| L (or U) | Unsupported length | Immersion length |
| d_root | Root diameter | Root outside diameter |
| d_tip | Tip diameter | Tip outside diameter |
| fw | Wake (Strouhal) frequency | Vortex-shedding frequency |
| fn | Natural frequency | Inherent frequency |
| r = fw / fn | Frequency ratio | Frequency ratio |
For loop integration after the calc passes, see our 4-20 mA wiring guide; for the matching temperature element, see sheathed thermocouples and RTD vs thermocouple selection.
Worked Example: Main Steam Line, 540 °C, 60 m/s
A boiler main steam header, DN200, carrying superheated steam at 540 °C and 12.5 MPa, average velocity 60 m/s. The proposed thermowell is 316SS, tapered, U = 250 mm, d_root = 25 mm, d_tip = 13 mm.
Step 1, Inputs. V = 60 m/s; ρ_steam at 540 °C / 12.5 MPa ≈ 37 kg/m³; μ_steam ≈ 3.1 × 10⁻⁵ Pa·s; P_max = 12.5 MPa; T_max = 540 °C.
Step 2, Reynolds and Strouhal. Re = 37 · 60 · 0.013 / 3.1 × 10⁻⁵ ≈ 9.3 × 10⁵. From the PTC 19.3 TW-2016 Strouhal table at this Re, St ≈ 0.226.
Step 3, Wake frequency. fw = 0.226 · 60 / 0.013 ≈ 1,043 Hz.
Step 4, Natural frequency. For 316SS, E = 193 GPa, ρ_material = 8,000 kg/m³. With d_root = 0.025 m, L = 0.250 m, K = 0.560:
Step 5, Ratio. fw / fn = 1,043 / 1,101 = 0.947. FAIL, exceeds the 0.8 transverse limit.
Step 6, Decision. Shorten U from 250 mm to 180 mm. New L² in the denominator drops by (250/180)² = 1.93, so fn rises to ≈ 2,125 Hz. New ratio fw / fn = 0.49 transverse pass, but 0.49 in-line still fails the 0.4 limit. Shorten further to 160 mm or increase d_root to 32 mm. With d_root = 32 mm and L = 180 mm, fn ≈ 2,720 Hz and the ratio drops to 0.38, passing both limits.
This is the typical iteration cycle on a main steam line. Sinopec refinery operators report similar wake-fail histories on vacuum tower overhead instrumentation, where the wells were originally specced from a generic 250 mm length without rerunning PTC 19.3 against the actual high-velocity vapor draw.
Three Ways to Pass a Failing Wake Frequency Check
When the calc fails, the fixes are well-ordered. We run them in this priority on every project:
- Shorten the unsupported length L. L appears squared in the fn denominator, so cutting it 20 % raises fn by 56 %. The cost is reduced sensor immersion. Verify the new L still places the sensor in the flowing fluid, not the boundary layer; the rule of thumb is at least 10 × d_tip immersion for representative readings.
- Increase the root diameter d_root. d_root appears linearly in fn. Going from 22 mm to 28 mm raises fn by 27 % and also raises bending stiffness, helping checks 2 and 3. The cost is heavier well, larger nozzle, slightly slower thermal response.
- Switch to a stiffer material. Going from 316SS (E = 193 GPa) to Inconel 625 (E = 207 GPa) raises fn by only 4 %, and the material is several times the cost. Almost always cheaper to redesign geometry first.
A fourth option, a velocity collar or vortex-suppression sleeve, works but requires support from the OEM's mechanical engineering team and is rare on field retrofits. We use it only when neither L nor d_root can move further.
When You Must Re-Run the Calculation
The calculation is not a one-time spec-sheet stamp. JJG 229-2010 Verification regulation for industrial platinum and copper resistance thermometers, the Chinese metrology equivalent, explicitly requires recertification of the sensor-plus-thermowell assembly under any of:
- Process velocity change greater than 10 %
- Media change (gas-to-liquid, single-phase-to-two-phase, viscosity drift)
- Thermowell dimensional modification (machining, repair, replacement)
- Detected vibration anomaly above background
The ASME standard lists no regulatory trigger, but the field practice is the same. Treat each condition as a mandatory recalc event.
Three Failure Modes We See in the Field
The textbook calc covers the math. The field tells you what actually breaks.
In-line resonance fatigue. Most common on high-velocity gas lines. The well vibrates parallel to flow at half the transverse Kármán frequency. The 0.4 in-line limit catches this, but online calculators that only check 0.8 transverse miss it. Crack initiates at the root weld toe.
Transverse Kármán fatigue. Classic case on steam and refinery vapor lines when L is too long. Crack propagates around the circumference at the root weld. The well snaps off cleanly and goes downstream.
Static overload. Less common but present on water-hammer-prone lines and process upsets. The well bends or buckles rather than fatigues. Usually a sign that the calc was run with steady-state velocity and missed the transient spike.
For shared-vibration deployments, see our high-temperature pressure transducer guide and the bimetallic temperature gauge working principle for the mechanical alternative.
Tools and Standards to Bookmark
These are the references we keep open during a wake-frequency check:
- ASME PTC 19.3 TW-2016: the U.S. standard, mandatory on most EPC contracts. The 2016 revision added the variable Strouhal number and the in-line resonance check.
- GB/T 30121-2013 (Industrial-platinum and copper resistance thermowells — protection tubes): the Chinese national standard, functionally equivalent on the geometry and frequency math.
- NIST Engineering Reference on pressure and vacuum measurements: the U.S. metrology source for property tables used in step 1.
- WIKA Wake Frequency Calculator: free web tool that follows PTC 19.3 TW-2016, decent for first-pass sizing.
- Ashcroft Wake Frequency Calculator: same calculation lineage, different interface; good cross-check.
For a temperature-cluster overview that maps thermowell to its sensor partner, see our industrial temperature sensor selection guide and the LIVE thermowells category page.
FAQ
What is wake frequency in a thermowell?
It is the frequency at which Kármán vortices shed off the back of the thermowell as fluid flows past. The calculation prevents that frequency from resonating with the well's natural frequency.
What is the formula for thermowell wake frequency?
fw = St · V / d, where St is the Strouhal number (≈ 0.22 for most industrial flows, but variable with Reynolds per PTC 19.3 TW-2016), V is flow velocity, and d is the thermowell tip diameter.
What is the maximum allowable frequency ratio for a thermowell?
0.8 for steady-state transverse resonance and 0.4 for in-line resonance per ASME PTC 19.3 TW-2016. Both limits must clear.
Is there a Chinese equivalent of ASME PTC 19.3 TW?
Yes. GB/T 30121-2013 (Industrial-platinum and copper resistance thermowells — protection tubes) covers the same calculation framework with Chinese nomenclature.
How do I shorten a thermowell to pass the wake frequency check?
L appears squared in the fn formula, so a 20 % reduction raises fn by 56 %. Verify the new immersion is still at least 10 × tip diameter so the sensor stays in the bulk flow.
Need a Thermowell That Passes the Calc?
Send your line spec (velocity, density, pressure, temperature, pipe ID, target sensor type) and we will run PTC 19.3 TW-2016 for you and quote a matched HMK thermowell plus its temperature element. Request a wake-frequency check. For the full product family, see our thermowells category and the industrial temperature sensor selection guide.
