flow-induced-vibration

name	flow-induced-vibration
description	Flow-induced vibration (FIV) — vortex-induced vibration (VIV), acoustic resonance, Strouhal number, Connors equation, tube bundle fluidelastic instability, ASME STS-1, lock-in avoidance, heat exchanger tubing, piping vibration.
metadata	{"priority":7,"promptSignals":{"phrases":["flow induced vibration","vortex induced vibration","fluidelastic instability","Strouhal number vibration","tube bundle vibration","acoustic resonance pipe"],"minScore":3}}

Flow-Induced Vibration (FIV) — Complete Skill

Vortex-Induced Vibration (VIV)

Strouhal Number and Vortex Shedding

Vortex shedding frequency: f_s = St × U / D [Hz; St = Strouhal number; U = free-stream velocity [m/s]; D = diameter [m]]

Strouhal number by Reynolds number:

• Re = 10²–2×10⁵: St ≈ 0.21 (circular cylinder, Kármán vortex street)
• Re = 2×10⁵–10⁷: St ≈ 0.27 (after turbulent transition)
• Rectangular cross-section: St ≈ 0.12–0.15 (depends on aspect ratio)

Lock-in (resonance condition): Occurs when f_s ≈ f_n (structural natural frequency) Lock-in range: U_r = U/(f_n × D) = 4–8 for circular cylinders Within lock-in: vortex shedding frequency locks to f_n; amplitude grows to A/D ≈ 0.5–1.5

Reduced velocity for avoidance: U_r = U/(f_n × D); keep U_r < 3.5 or U_r > 9 to avoid lock-in

Scruton number (mass-damping parameter): Sc = 4π × m_s × ζ / (ρ_f × D²) [m_s = structural mass per unit length; ζ = damping ratio] Sc > 20: VIV amplitude < 0.05D (negligible); Sc < 2: severe VIV risk

VIV Amplitude Prediction

Griffin curve (empirical): A/D = f(Sc) from Griffin-Koopmann data A/D ≈ 0.07/√(Sc + 0.07) [approximate; from Scruton-Griffin plot]

Force model (Morison equation for offshore risers): F(t) = (1/2) ρ_f U² D C_D + ρ_f (π/4)D² C_M × a_fluid [C_D = drag; C_M = inertia; a = fluid acceleration] VIV lift force: F_L = (1/2) ρ_f U² D C_L sin(2πf_s t) [C_L ≈ 0.3–0.5 at lock-in]

Fluidelastic Instability (Tube Bundles)

Critical for heat exchanger tube arrays in crossflow (steam generators, condensers)

Connors Equation (Threshold for Instability)

Critical velocity: U_c / (f_n × D) = K × √(2π ζ m_s / (ρ_f D²)) K = instability constant; K ≈ 4.0 for triangular pitch array; K ≈ 3.0 for square pitch m_s = mass per unit length (including virtual mass of fluid in tube) ζ = structural damping ratio (typically 0.003–0.02 for heat exchanger tubes)

Safety criterion: U_gap / (f_n × D) ≤ 0.5 × K × √(2π ζ m_s / (ρ_f D²)) Use 50% of critical velocity as design limit; factor of safety = 2.0 on velocity → 4.0 on force

Gap velocity calculation: U_gap = U_∞ × P / (P - D) [P = tube pitch; D = tube diameter]

Mass Parameter and Damping

Effective mass per unit length (tube + internal fluid + virtual fluid): m_s = m_tube + m_internal_fluid + m_virtual [kg/m] m_virtual = ρ_f × π/4 × D² × C_M [added mass; C_M ≈ 1.5 for tube in bundle]

Damping in liquid (baffle-to-baffle): ζ_total = ζ_structural + ζ_fluid [ζ_fluid = squeeze film damping at baffles ≈ 0.005–0.02]

Lift force in post-instability: F_L = ρ_f U_gap² D C_L_fluid [not well-characterized; design to avoid instability, not predict post-critical]

Acoustic Resonance in Piping

Standing wave frequencies in cylindrical pipe: f_n = n × c / (2L) [closed-closed or open-open; n = 1,2,3,...; c = speed of sound; L = pipe length] f_n = (2n-1) × c / (4L) [open-closed; compressor suction or discharge lines]

Acoustic resonance with vortex shedding: Resonance when f_s ≈ f_acoustic_mode → large pressure oscillations Commonly at: orifices, branch connections, valve cavities, closed side branches

Side branch (stub pipe) resonance: f_n = (2n-1) × c / (4L_stub) [n = 1,2,...; open-closed stub] Excitation Strouhal number: St = f × d / U = 0.3–0.6 (d = stub diameter)

Prevention: stagger branch locations; add acoustic damping; detune by changing stub length; use baffles

Speed of Sound in Piping

Speed of sound in fluid with pipe wall compliance: c_effective = c_fluid / √(1 + ρ_fluid c_fluid² D / (E_pipe t)) c_fluid (water) = 1480 m/s; c_fluid (natural gas, 15°C) = 420 m/s; c_fluid (air) = 340 m/s

Compressor/blower system resonance: Check: blade passing frequency (BPF = N_blades × RPM/60) vs. acoustic modes of connected piping Separation: |f_BPF - f_acoustic| ≥ 15% × f_acoustic

Piping Vibration Assessment

ASME OM-3 (piping vibration limit): Continuous vibration limit: 12.7 mm/s (0.5 in/s) peak velocity for carbon steel piping Allowable displacement: δ_allow = σ_endurance × (OD/2) / (E × κ × √(f/f_ref))

Energy Institute Guidelines (EI): Screening: displacement x [mm] and frequency f [Hz] x × f² < 0.4 m/s² for low-pressure piping → acceptable (zone A) x × f² = 0.4–2 m/s² → inspection required (zone B) x × f² > 2 m/s² → corrective action (zone C)

Piping natural frequency (simply supported span): f = (π/2) × √(EI/(m_eff × L⁴)) × (1/2π)^(-1) [Hz; simplified beam formula] Or: use published span tables from B31.3/ASME

Common excitation sources in piping:

• Reciprocating compressor: pulsation at multiples of RPM/60 × number of cylinders
• Centrifugal pump: impeller blade passing frequency
• Control valves: turbulent noise (high-frequency broadband)
• Two-phase flow: slug flow at 1–10 Hz (large slugs)
• Thermal cycling: low-frequency thermal expansion cycling

Heat Exchanger Tube Design

Tube natural frequency (clamped-clamped, multiple spans): f₁ = (π/2L²) × √(EI/m_eff) [Hz; L = longest unsupported span between baffles] For multiple baffles: effective frequency uses longest unsupported span

Baffle spacing (TEMA): Minimum baffle spacing: 1/5 of shell ID or 50 mm (whichever is greater) Maximum: specified by TEMA based on unsupported tube span limits

Tube support gap: 0.4–0.8 mm clearance (prevents tube-baffle wear while allowing thermal expansion)

TEMA vibration limits: U_gap/U_c < 0.5 (Connors criterion with K = 4.0) If exceeded: add intermediate supports, stiffen tubes, change pitch

Standards

Standard	Scope
ASME STS-1	Steel stacks — flow-induced vibration
ASME OM-3	Piping vibration assessment
TEMA Standards	Heat exchanger tube vibration
API 618	Reciprocating compressors — pulsation/vibration
Energy Institute 2008	Guidelines for control of flow-induced vibration
DNV-RP-F105	Free-spanning submarine pipelines (VIV)

Output

Provide: mechanism identified (VIV/fluidelastic/acoustic resonance/piping vibration), geometry (D [mm], L [m], pitch P [mm]), flow velocity U [m/s] and gap velocity U_gap [m/s], Strouhal frequency f_s [Hz], structural natural frequency f_n [Hz], reduced velocity U_r and Scruton number Sc, lock-in check (U_r in range 4–8?), Connors critical velocity U_c [m/s] and safety ratio U_gap/U_c, acoustic resonance check (f_s vs. f_acoustic [Hz]), predicted amplitude A/D (Griffin curve), piping vibration level (EI zone A/B/C), corrective action if required (add support/detune/increase damping), and applicable standard (ASME STS-1, TEMA, API 618).