Wake Frequency Calculation for Thermowells (ASME PTC 19.3 TW-2016)

Published • ~14–18 min read

Thermowells protect temperature sensors from harsh process conditions—but they also introduce a bluff body into the flow. That means vortex shedding, dynamic forces, and the potential for damaging resonance. ASME PTC 19.3 TW-2016 codifies how to evaluate these risks. This practical guide demystifies the wake frequency calculation, the inputs you need, the equations behind the checks, and design strategies that reliably lead to code-compliant, robust thermowells.

What Is Wake Frequency and Why It Matters

When fluid flows past a cylindrical body such as a thermowell, it sheds vortices alternately from each side. This periodic shedding creates an oscillating lift force at a characteristic frequency—commonly called the wake or vortex shedding frequency. If that forcing frequency approaches one of the thermowell’s natural frequencies, vibration can amplify dramatically.

Wake (vortex shedding) frequency is the periodic detachment of vortices in the body’s wake, producing alternating lift forces that act transverse to flow.
Resonance risk: When the wake frequency approaches the thermowell’s in-situ natural frequency, the structure can resonate, elevating stresses and risking fatigue failure, process leaks, or sensor damage.
ASME PTC 19.3 TW-2016 provides a standardized calculation method and acceptance criteria to maintain adequate separation between excitation and natural frequencies, including allowances for damping and in-line excitation.

Rule of thumb: keep sufficient separation between the shedding frequency and the first lateral natural frequency after considering damping, in-line excitation, and process velocity variability.

Key takeaway

Wake frequency is inevitable; resonance is optional. Good geometry choices and adherence to ASME PTC 19.3 TW-2016 keep the natural frequency sufficiently away from the excitation range across all credible operating velocities.

Key Inputs Required by ASME PTC 19.3 TW-2016

Gather accurate, temperature-relevant inputs before you run the calculation. Missing or ambient-property data is a leading cause of false failures or, worse, unsafe approvals.

1) Process conditions

Fluid density (ρ), dynamic viscosity (μ), bulk temperature, pressure
Steady-state velocity profile or line average velocity; if unknown, supply mass flow rate and pipe ID to compute it
Velocity ranges: minimum, normal, and maximum (including start-up and upset cases)

2) Thermowell geometry

Shank profile: straight, tapered, or stepped
Outside diameter (Do), bore diameter (Db), root diameter, tip diameter
Insertion length (U), from the process connection to the tip; fillet radii and taper details

3) Mounting details

Connection: flanged, threaded, or weld-in
Support conditions: stiffness at the root, effective clamping length, gasket thickness (for flanged)
Pipe size and schedule (influences blockage and local flow)

4) Material properties at operating temperature

Modulus of elasticity (E), density (ρs)
Allowable stress and fatigue properties for code checks

5) Environmental factors

Cavitation likelihood, two-phase or pulsating flow
Acoustic resonance risk and nearby fittings that can alter local velocity

Material selection affects dynamics and survivability

Higher modulus materials increase stiffness and natural frequency, while corrosion-resistant alloys extend service life. For guidance on matching materials to corrosive duty, see the related post: protection tube material selection for sensors.

Core Equations: From Vortex Shedding to Natural Frequency

The ASME method combines fluid dynamics and structural dynamics. The goal is to quantify excitation (vortex shedding and in-line) and compare it to the in-situ natural frequency with appropriate margins and damping.

Vortex shedding frequency

The fundamental relationship is f_w = St × U / Do, where U is approach velocity and Do is the thermowell’s characteristic diameter exposed to the flow (typically the shank diameter at the shedding location). The Strouhal number St depends on Reynolds number and surface condition; in the subcritical regime for smooth circular cylinders it is often close to 0.2, but code correlations should be used.

Reynolds number and regime

Reynolds number Re = ρ U Do / μ characterizes the flow regime. ASME PTC 19.3 TW-2016 references appropriate St–Re correlations to obtain St. Ensure μ and ρ are taken at process temperature and pressure.

Natural frequency in-situ

The thermowell is modeled as a cantilevered beam with the process connection acting as the support. The in-situ first lateral natural frequency considers:

Geometric stiffness from the shank profile (taper raises stiffness without excessive blockage)
Added mass of the displaced fluid, which lowers the frequency
Mounting compliance at the root

The result is the first lateral natural frequency f_n for cross-flow response; in-line (axial) excitation is also checked because the lift force has a component at approximately twice the shedding frequency.

Damping and amplification

Damping (structural plus fluid) limits the vibration amplitude at resonance. If measured damping is unavailable, the code prescribes default values. Lower damping increases the required separation margin because dynamic amplification is higher near resonance.

Separation criteria

ASME PTC 19.3 TW-2016 specifies minimum separation ratios between the forcing frequencies (cross-flow and in-line) and the in-situ natural frequency after accounting for damping and velocity variation. The check is performed at minimum, normal, and maximum velocities.

Engineer’s checkpoint

Use temperature-corrected E and μ, apply the correct St–Re correlation, and treat in-line excitation explicitly. These three items account for a large share of unexpected calculation failures.

Step-by-Step Calculation Workflow

Use this structured workflow to generate a transparent, auditable thermowell calculation package that aligns with ASME PTC 19.3 TW-2016.

1) Define geometry and materials

Select shank type (tapered preferred when velocity is high) and define Do along the insertion, Db, root diameter, and fillet radii.
Specify insertion length U measured from the support plane to the tip.
Obtain material properties at operating temperature: E(T), ρs(T), allowable stress, and fatigue data if available.

2) Establish process properties and velocity

Compute density and dynamic viscosity at bulk temperature and pressure.
Derive line average velocity from flow rate and pipe ID; account for expected ranges (min/normal/max).
Calculate Re = ρ U Do / μ for each velocity case.

3) Determine Strouhal number and wake frequencies

Select the St–Re correlation per code guidance for smooth cylinders in the relevant Re range.
Compute cross-flow shedding frequency: f_w = St × U / Do for each velocity case.
Estimate in-line excitation frequency, often approximated near 2 f_w for lift/drag phenomena.

4) Compute in-situ natural frequencies

Model the thermowell as a cantilever with distributed mass and stiffness; include added fluid mass.
Evaluate the first lateral mode frequency f_n1; consider higher modes if insertion is long or supports are flexible.
Apply mounting compliance if the support is not perfectly rigid (e.g., gasketed flanges).

5) Apply damping and dynamic amplification

Use measured or literature-based structural damping; otherwise, apply ASME default damping.
Estimate dynamic amplification near resonance to determine expected vibration amplitudes.

6) Check frequency separation criteria

For each velocity case, check that f_n is sufficiently higher than f_w (cross-flow) and the in-line excitation per code margins.
Confirm that small changes in U or velocity do not collapse the margin (sensitivity check).

7) Verify stresses and fatigue per code

Compute drag and lift forces; derive bending moment at the root and maximum fiber stress.
Compare to allowable stresses; if cyclic, evaluate fatigue per code recommendations.

8) Iterate the design as needed

Shorten U, increase root diameter, or transition to a tapered shank.
Add a velocity collar or support ring when permitted and correctly located.
Re-check with revised geometry and updated St–Re values if Do changes.

Workflow summary

Compute Re → get St → calculate f_w → evaluate f_n in-situ with added mass and compliance → apply damping → check separation and stresses → iterate geometry. Keep a documented trail of each assumption and data source.

Common Design Adjustments to Achieve Compliance

When the initial design fails the separation or stress checks, these adjustments typically recover compliance efficiently:

Use tapered thermowells: Increase stiffness with minimal blockage increase, often yielding a higher f_n without large pressure drop penalties.
Reduce insertion length (U): Even modest reductions can significantly raise f_n. Consider offsets or angled insertion if measurement representativeness allows.
Increase root diameter: Improves section modulus and stiffness at the critical fixed end.
Material upgrade: A higher modulus at operating temperature raises f_n, while improved fatigue properties enhance durability.
Velocity collars/support rings: When permitted and correctly located, these add support and curtail vibration. Confirm installation tolerances.
Validate process velocities: Overly conservative max velocities can drive false failures; conversely, underestimation is unsafe. Align with credible worst-case scenarios.

Worked Example: Framing the Numbers

The following simplified, illustrative example demonstrates the logic flow. Always use full ASME correlations and detailed geometry in production calculations.

Inputs

Fluid: water at 90°C → ρ ≈ 965 kg/m³, μ ≈ 0.00032 Pa·s
Velocity cases: U = 1.5 / 3.0 / 4.5 m/s (min/normal/max)
Shank: tapered, with characteristic Do at shedding location ≈ 19 mm (0.019 m)
Insertion U-length: 230 mm; material: 316 SS with E(90°C) ≈ 180 GPa

Step A: Reynolds number

Re = ρ U Do / μ → at U = 3 m/s, Re ≈ (965 × 3 × 0.019) / 0.00032 ≈ 171,600 (subcritical regime).

Step B: Strouhal number and shedding

Use code correlation; assume St ≈ 0.2 for illustration. f_w = 0.2 × 3 / 0.019 ≈ 31.6 Hz (normal case). At U = 4.5 m/s, f_w ≈ 47.4 Hz.

Step C: In-situ natural frequency

Using a cantilever model with added mass, suppose f_n1 ≈ 80–90 Hz for the tapered geometry and support. This gives a nominal separation ratio at normal conditions: f_n1 / f_w ≈ 2.5–2.8.

Step D: In-line excitation

Approximate at ~2 f_w: 63–95 Hz across the velocity range. Check both cross-flow and in-line vs. f_n1; ensure margins per code after damping is applied.

Step E: Stresses

Estimate drag and lift forces with appropriate coefficients; verify bending stress at the root vs. allowable. If cyclic duty is significant, perform fatigue life estimation per code guidance.

Interpretation

If in-line excitation approaches f_n1 at maximum velocity, either shorten U or slightly increase root diameter to push f_n1 above the highest in-line frequency with margin.

Verification, Documentation, and Compliance Tips

Auditable calculations are a competitive advantage. They reduce design churn, clarify assumptions, and protect the project during reviews.

Document assumptions: Record fluid properties vs. temperature, chosen St–Re correlation, mounting stiffness assumptions, and any default damping values.
Sensitivity analyses: Vary velocity (±20%), density, and insertion length. Identify near-resonance edges and quantify safety margins.
As-built consistency: Confirm that the final drawing (root diameter, fillets, taper length, connection) matches the input model. Note flange rating, thread engagement, or weld-in length.
Complex flows: For non-Newtonian, cavitating, or two-phase flows, consider advanced methods (empirical tests or CFD) to refine St and force coefficients.
Traceability: Align part numbers, revision control, and MTRs with the finalized calculation package.

Practical Notes Engineers Often Overlook

Surface condition matters: Roughness or fouling can shift effective St and drag coefficients; incorporate realistic allowances.
Nearby fittings: Elbows, reducers, and tees close to the thermowell distort velocity and turbulence; reassess U and Re locally.
Temperature gradients: If the shank spans hot/cold regions, E(T) changes along the length; conservative use of the lower E can be appropriate.
Sensor mass: Heavy inserts and transmitters add mass at the tip; include their effect when significant.
Gasket compliance: For flanged wells, soft gaskets reduce support stiffness—lowering f_n.

Quality Checks Before Release

Units sanity: Confirm consistent SI or Imperial units throughout, including E, μ, and density.
Velocity coverage: Validate min/normal/max and any transient (start-up, trip) states.
Mode shape appropriateness: Ensure the first lateral mode is governing; check higher modes for long insertions.
In-line and cross-flow: Demonstrate both are within acceptable margins, not just cross-flow.
Stress plus vibration: Combine dynamic amplification where appropriate; verify against allowable stress and fatigue.

Troubleshooting Noncompliance

When a design fails, focus on high-leverage changes first.

Too close to resonance at max velocity: Shorten U by 10–20% or increase root diameter. Evaluate a tapered profile if currently straight.
In-line excitation conflict: Target a separation margin specifically at ~2 f_w; modest stiffness gains often solve it.
Excessive dynamic stress: Add a support ring or collar where permitted; confirm installation tolerances and thermal expansion effects.
Uncertain properties: Recompute with temperature-corrected μ and E; this alone can swing results.

FAQ: ASME PTC 19.3 TW-2016 Wake Frequency

Is St always 0.2?

No. While 0.2 is typical in a subcritical regime for smooth cylinders, the code uses correlations dependent on Reynolds number. Always calculate St from Re using the prescribed relationship.

Do I need CFD?

Usually not. The ASME method is robust for single-phase, fully developed flows. Consider CFD for complex geometries, two-phase flow, or when nearby fittings alter local velocity significantly.

What if I can’t change insertion length?

Switch to a tapered shank, increase root diameter, or evaluate a velocity collar/support ring. Also reassess conservative assumptions and verify actual maximum velocity.

How do material choices affect vibration?

Higher modulus increases stiffness and natural frequency; density shifts mass distribution. Corrosion resistance affects surface roughness over time, preserving expected St. For guidance on material durability, see this protection tube material guide.

Conclusion: Designing Thermowells that Stay Clear of Resonance

ASME PTC 19.3 TW-2016 provides a proven, auditable framework to avoid resonance-driven failures. The essence of compliance is straightforward:

Use temperature-corrected properties to compute Re and select the correct St.
Calculate wake frequencies across the full velocity envelope and include in-line excitation.
Determine in-situ f_n with added mass and mounting compliance.
Apply damping and verify code separation and stress limits.
Iterate geometry—taper, root diameter, and insertion length—until margins are robust.

When in doubt, prioritize tapered shanks, realistic velocity assumptions, and thorough documentation. For materials under corrosive service, complement your analysis with informed selection—our related resource on choosing protection tube materials is a helpful starting point.

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