Wake Frequency Analysis and ASME PTC 19.3 TW-2016: Preventing Vortex-Induced Vibration

What Is Wake Frequency Analysis?

When a cylindrical object such as a thermowell or sample probe assembly is immersed in a flowing fluid, it creates alternating vortices that shed from either side of the cylinder in a pattern known as a Von Karman vortex street. These vortices generate periodic lateral forces on the probe at a specific frequency called the vortex shedding frequency (fs). If this frequency approaches the natural mechanical frequency (fn) of the probe, resonance can occur, leading to excessive vibration amplitudes, fatigue cracking, and ultimately catastrophic failure.

Wake frequency analysis is the engineering calculation performed to verify that a given probe or thermowell design will not experience dangerous vortex-induced vibration (VIV) under expected process conditions. This analysis is not optional for critical installations. It is a fundamental safety and reliability step mandated by industry standards for any cylindrical element inserted into a flowing process stream.

The Governing Standard: ASME PTC 19.3 TW-2016

The authoritative reference for wake frequency analysis of thermowells and sample probes is ASME PTC 19.3 TW-2016, titled "Thermowells -- Performance Test Codes." Published by the American Society of Mechanical Engineers, this standard replaced the earlier 2010 edition and provides a comprehensive methodology for evaluating:

1. Frequency ratio (fs/fn): The ratio of vortex shedding frequency to natural frequency

2. Static stress: Drag-induced bending stress on the probe

3. Dynamic stress: Resonance-amplified cyclic stress

4. Hydrostatic pressure stress: External pressure acting on the probe tip

The 2016 revision introduced several updates, including revised Strouhal number correlations, updated damping factors, and refined criteria for distinguishing between in-line and transverse resonance modes. While the standard is written for thermowells, the same physics and calculation methodology apply directly to sample probe assemblies, which share the same cantilevered-cylinder geometry.

The Strouhal Number and Vortex Shedding Frequency

The Strouhal number (St) is a dimensionless parameter that relates the vortex shedding frequency to the fluid velocity and the cylinder diameter. For cylinders in the subcritical Reynolds number range typical of most process applications, the Strouhal number is approximately constant:

St = 0.22 (typical value for cylindrical probes)

The vortex shedding frequency is calculated using the fundamental relationship:

fs = St x V / d

Where:

fs = vortex shedding frequency (Hz)
St = Strouhal number (dimensionless, approximately 0.22)
V = free-stream fluid velocity (ft/s or m/s)
d = outside diameter of the probe or thermowell at the tip (ft or m)

This equation is the starting point for every wake frequency analysis. Higher fluid velocities and smaller probe diameters produce higher shedding frequencies. The engineer must then compare this shedding frequency to the natural frequency of the probe to determine whether resonance is a concern.

Natural Frequency of the Probe

The natural frequency (fn) of a thermowell or sample probe depends on its geometry and material properties. For a tapered or straight cantilevered cylinder, the natural frequency is governed by:

Unsupported length (L): The distance from the mounting root to the probe tip
Outside diameter (D) and inside diameter (d): Determining the moment of inertia
Material modulus of elasticity (E): Stiffness of the alloy
Material density: Combined with added mass effects from the surrounding fluid

Longer, thinner probes have lower natural frequencies. Shorter, thicker probes have higher natural frequencies. This relationship is central to every redesign strategy when a probe fails the wake frequency check.

The fs/fn Ratio: Pass/Fail Criteria

The critical output of the ASME PTC 19.3 analysis is the frequency ratio fs/fn. The standard establishes the following limits:

fs/fn less than 0.80: The probe passes the wake frequency check. There is sufficient separation between the shedding frequency and the natural frequency to avoid resonance amplification.
fs/fn equal to or greater than 0.80: The probe fails. The design is too close to resonance and must be modified.

The 0.80 threshold provides a safety margin to account for uncertainties in flow velocity, fluid properties, and manufacturing tolerances. Some operators apply even more conservative limits (such as 0.75) for critical or safety-instrumented installations.

It is important to note that the analysis must be performed at the maximum expected flow velocity, not the normal operating velocity. Upset conditions, blowdown scenarios, and emergency depressurization events can produce velocities far exceeding normal operation, and the probe must survive these transient conditions without entering resonance.

What to Do When a Probe Fails the Wake Frequency Check

When a sample probe or thermowell design fails the ASME PTC 19.3 analysis (fs/fn exceeds 0.80), the engineer has several redesign strategies available. Each approach works by either reducing the shedding frequency or increasing the natural frequency to restore an acceptable frequency ratio.

Reduce Insertion Length

Shortening the unsupported length of the probe is the single most effective way to increase the natural frequency. Because fn scales inversely with the square of the length, even a modest reduction in insertion depth produces a significant increase in fn. The tradeoff is that the probe tip may no longer reach the center third of the pipe, potentially compromising sample representativeness.

Increase the Outside Diameter

Using a larger OD probe tube or thermowell increases the moment of inertia, which raises the natural frequency. A common upgrade path is moving from 1/2-inch OD tubing to 3/4-inch OD, or from 3/4-inch to 1-inch OD. The larger diameter also slightly reduces the shedding frequency (since fs is inversely proportional to d), providing a dual benefit.

Install a Support Collar (Velocity Collar)

A support collar or velocity collar is a bushing or sleeve installed at the process connection that effectively shortens the unsupported cantilever length. The collar acts as a secondary support point, dramatically increasing the natural frequency without changing the insertion depth. This is often the preferred solution when the probe must maintain its full insertion length for representative sampling.

Use a Tapered Shank Design

Tapered thermowells and probes have a larger root diameter that transitions to a smaller tip diameter. This geometry increases stiffness at the root where bending stresses are highest while maintaining a smaller tip diameter that minimizes flow disruption. ASME PTC 19.3 TW-2016 includes specific provisions for analyzing tapered designs.

Reduce Flow Velocity

In some cases, the process design can be modified to reduce the fluid velocity at the probe location. Relocating the probe to a larger-diameter pipe section, moving it upstream of a restriction, or adding a flow straightener are all viable approaches when mechanical redesign alone is insufficient.

When Is Wake Frequency Analysis Required?

Wake frequency analysis should be performed for every thermowell and sample probe assembly installed in a flowing process stream. It is especially critical in the following scenarios:

High-velocity gas service: Gas pipelines and compressor discharge lines where velocities can exceed 100 ft/s
Long insertion depths: Probes extending into large-diameter pipes (12 inches and above) where unsupported lengths become significant
Lightweight probe designs: Small-diameter thin-walled tubing that has inherently low natural frequencies
Safety-critical installations: Any probe whose failure could cause a loss of containment, environmental release, or hazard to personnel

Process engineers should request wake frequency analysis documentation from the probe manufacturer before finalizing any installation in moderate-to-high velocity service. A compliant analysis per ASME PTC 19.3 TW-2016 provides the documented assurance that the probe will withstand the dynamic loading imposed by vortex shedding throughout its service life.