Shell-and-Tube Heat Exchanger Flow-Induced Vibration Case Study

A shell-and-tube heat exchanger can meet heat-duty requirements and still be mechanically unsafe. When shell-side flow crosses the tube bundle, fluctuating fluid forces can excite tubes, wear support holes, create fretting scars, and eventually produce tube leaks. The failure may first appear as a process contamination event rather than as a mechanical vibration alarm.

This case study follows a process cooler whose cooling-water flow was increased after a debottlenecking change. The exchanger recovered thermal duty, but two weeks later operators found a small tube leak and a narrow-band vibration component near the tube natural frequency. The engineering task is to decide whether the exchanger can keep operating, whether fouling or corrosion is the root cause, and what correction is required before release.

The calculations are screening calculations for engineering judgement. A real exchanger assessment should use the exchanger mechanical design code, tube layout, baffle geometry, fluid properties, two-phase checks, acoustic resonance checks, vendor vibration criteria, inspection data, metallurgy, corrosion history, pressure-boundary requirements and qualified mechanical review.

Case Context

A shell-and-tube exchanger cools a hydrocarbon process stream on the tube side using water on the shell side. After a production increase, cooling-water flow was raised to restore outlet temperature. The heat duty improved, but vibration noise increased near the exchanger shell, and a conductivity monitor later indicated water ingress into the process side.

Inspection during a short outage found shiny fretting marks at several baffle support holes and one leaking tube near the middle baffle span.

The central question is:

Did the increased shell-side crossflow create a tube-vibration condition that must be corrected before the exchanger is returned to service?

Field Data

Quantity	Symbol	Value
shell-side volumetric flow rate	Q_s	0.210\ \text{m^3/s}
effective crossflow area through bundle window	A_c	0.075\ \text{m^2}
tube outside diameter	D_o	19.0\ \text{mm}
tube inside diameter	D_i	15.7\ \text{mm}
unsupported tube span between baffles	L	0.75\ \text{m}
tube elastic modulus	E	190\ \text{GPa}
tube metal density	\rho_m	8000\ \text{kg/m^3}
internal liquid density	\rho_i	1000\ \text{kg/m^3}
external added-mass coefficient	C_a	1.0
external liquid density	\rho_o	1000\ \text{kg/m^3}
screening Strouhal number	St	0.22
estimated damping ratio in liquid	\zeta	0.01
measured narrow-band vibration component		65\ \text{Hz}
baffle-hole diametral clearance		0.25\ \text{mm}
observed peak tube motion near support		0.35\ \text{mm}

The velocity is an effective crossflow value, not a shell-nozzle velocity. In real exchanger work, crossflow velocity depends on baffle cut, tube pitch, leakage streams, bypass lanes, pass layout, fouling, and local maldistribution.

Field Evidence

Evidence	Engineering interpretation
thermal duty improved after flow increase	fouling was not the only active issue
leak location is near a baffle support	support fretting is plausible
shiny wear marks appear at tube support holes	relative tube/support motion occurred
vibration peak appears near 65\ \text{Hz}	tube natural frequency or excitation harmonic is plausible
no broad corrosion field is seen on inspected tubes	general corrosion is less likely as primary root cause
leak appeared after shell-side flow increase	flow-induced vibration is credible

The diagnosis should not depend on one frequency line. It should connect flow change, excitation frequency, tube natural frequency, support wear, leak location and post-correction validation.

Step 1: Calculate Shell-Side Crossflow Velocity

Use the continuity equation:

Substitute:

and:

Then:

Engineering Comment

This is the velocity that matters for tube excitation. A heat-duty calculation may show that more cooling water is beneficial, while the mechanical review shows that the same flow increase moves the exchanger into a vibration-sensitive regime.

Step 2: Estimate Vortex-Shedding Frequency

A first-pass shedding frequency is:

Use:

Then:

The second harmonic is:

Engineering Comment

The measured vibration component near 65\ \text{Hz} is consistent with a harmonic of the shedding excitation. The exact mechanism may include turbulent buffeting, fluidelastic coupling, support looseness, or acoustic interaction, but this frequency match is enough to justify a mechanical vibration review.

Step 3: Estimate Tube Mass per Unit Length

Tube metal area:

Tube metal mass per unit length:

Internal fluid area:

Internal fluid mass:

External added mass screen:

Total vibrating mass per unit length:

Engineering Comment

Ignoring fluid mass would overestimate natural frequency. Tubes in liquid do not vibrate like dry beams in air.

Step 4: Estimate Tube Natural Frequency

The second moment of area for the tube wall is:

Flexural stiffness:

For a simply supported screening model:

With:

the result is:

Engineering Comment

The estimated first tube natural frequency is essentially coincident with the measured vibration component and with the second shedding harmonic. This is a poor separation margin.

Step 5: Calculate Frequency Separation

The excitation ratio is:

The frequency separation from the tube natural frequency is:

or:

Engineering Comment

This is not an acceptable screening separation. A practical design normally needs a conservative separation allowance because flow velocity, fluid density, temperature, support condition, fouling, baffle looseness and model uncertainty can shift both excitation and response frequencies.

Step 6: Estimate Dynamic Amplification

For a simplified single-degree-of-freedom response, the dynamic amplification factor is:

Using:

and:

gives:

Engineering Comment

The absolute DAF is model-sensitive, but the message is robust: a lightly damped tube close to resonance can amplify small flow-force fluctuations into support contact, fretting and fatigue damage.

Step 7: Compare Motion With Support Clearance

Observed peak tube motion near the support is:

Baffle-hole diametral clearance is:

The motion-to-clearance ratio is:

Engineering Comment

The tube can contact the support hole during vibration. Once contact begins, the problem is not just elastic stress. Fretting wear can remove material locally, create stress raisers and initiate leakage or fatigue cracking.

Step 8: Evaluate a Support Correction

A corrective baffle or support change reduces the unsupported span to:

For the same tube and fluid mass, natural frequency scales approximately with:

So:

New frequency ratio:

New dynamic amplification:

Engineering Comment

The support correction moves the tube away from the excitation harmonic and strongly reduces dynamic amplification. The final design should still check pressure drop, cleanability, thermal expansion, vibration in other spans, tube support wear, bypass flow and maintainability.

Engineering Decision

The exchanger should not be returned to unrestricted service in the original high-flow configuration. The evidence supports flow-induced tube vibration with support fretting risk.

The decision is:

Hold unrestricted operation, plug or replace damaged tubes as required by pressure-boundary rules, reduce shell-side flow or add support correction, verify tube natural-frequency separation, inspect adjacent spans for fretting, and release only after vibration and leak-test evidence confirm stable operation.

If production requires temporary operation, it should use a restricted cooling-water flow that keeps excitation away from the critical response region and should include leak monitoring, vibration trending and defined shutdown triggers.

Failure Modes and Controls

Failure mode	Evidence	Control
higher cooling-water flow excites tube vibration	frequency match after flow increase	crossflow and vibration screen before debottlenecking
tube/support fretting produces leak	shiny wear scars at baffle holes	support redesign, tube plugging or replacement
fouling diagnosis hides mechanical damage	heat duty improves but leak appears	inspect tube supports, not only UA and pressure drop
model ignores added fluid mass	natural frequency overestimated	include tube, internal fluid and added mass
local bypass or maldistribution raises velocity	damage concentrated near one window	inspect baffle seals, pass partition and bypass lanes
support correction creates thermal stress or pressure-drop issues	added support changes mechanical boundary	review thermal expansion, pressure drop and maintenance access

Risk Review

Risk item	Severity	Occurrence	Detection	RPN
continuing high-flow operation with tube fretting	8	4	5	160
treating the event as fouling only	7	4	6	168
plugging leaking tube without correcting vibration	8	3	6	144
support modification without thermal and pressure-drop review	6	3	4	72

The controls reduce occurrence and improve detection: velocity screening, frequency separation, vibration trending, eddy-current or borescope inspection, pressure test, leak monitoring, and mechanical review of support changes.

Release Criteria

Release should require evidence that the exchanger is thermally useful and mechanically stable.

Criterion	Required evidence
damaged tubes	leak source identified, plugged or replaced under pressure-boundary procedure
tube support condition	baffle holes and adjacent tubes inspected for fretting
flow condition	shell-side flow limit or support modification documented
frequency separation	excitation frequencies separated from tube natural frequencies with conservative allowance
vibration response	measured vibration below site limit at maximum approved flow
heat-duty performance	exchanger still meets required duty after flow or support correction
pressure drop	shell-side and tube-side pressure drops remain acceptable
process safety	cross-contamination monitoring and pressure test are passed
follow-up trend	vibration, leak indication and duty are monitored after restart

Transferable Lessons

A heat exchanger is both a thermal device and a mechanical structure. Increasing flow may solve a heat-duty problem while creating a vibration problem.

The practical workflow is:

1. identify the operating change that increased flow or velocity;
2. calculate effective crossflow velocity through the tube bundle;
3. estimate shedding or excitation frequency;
4. estimate tube natural frequency including fluid mass;
5. check separation and dynamic amplification;
6. inspect supports for fretting and leaking tubes;
7. correct span, support, flow or bundle configuration;
8. release only after thermal, mechanical and process-containment evidence agree.

This case is distinct from a fouling duty-shortfall case. Fouling asks whether heat-transfer resistance and pressure drop have reduced duty. Flow-induced vibration asks whether the exchanger geometry and flow velocity are exciting tubes strongly enough to create mechanical wear, fatigue and leaks.