[ f_n = \frac\lambda^22\pi L^2 \sqrt\fracEIm ]

(simplified uniform beam): ( I = \frac\pi (d_root^4 - d_bore^4)64 ) (assume bore dia 6 mm → 0.006 m) ( I ≈ 8.9 × 10^-8 , m^4 ) ( m_metal = \rho_m × \textcross-sectional area ≈ 8000 × 7.85e-4 = 6.28 , kg/m ) ( m_added = 1000 × 4.91e-4 = 0.49 , kg/m ) ( m_total = 6.77 , kg/m )

If the frequency of these vortices coincides with the natural frequency of the thermowell, occurs. This can cause large-amplitude vibrations, leading to fatigue failure, fracture, and loss of process containment.

determines the vortex shedding frequency and compares it to the thermowell’s natural frequency to ensure safe operation. 2. Governing Physics 2.1 Strouhal Number (St) The dimensionless Strouhal number relates vortex shedding frequency to flow velocity and thermowell diameter: