Thermowell Wake Frequency Calculation !exclusive! -

(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 )

[ f_n = \frac\lambda^22\pi L^2 \sqrt\fracEIm ] thermowell wake frequency calculation

Industry standards (ASME PTC 19.3 TW) require: [ f_w \le 0.8 f_n \quad \textor \quad f_w \ge 1.2 f_n ] (i.e., at least 20% separation margin) Step 1: Gather Input Data | Parameter | Symbol | Typical Value | |-----------|--------|----------------| | Fluid density | ρ | 1000 kg/m³ (water) | | Fluid velocity | V | 5 m/s | | Tip diameter | d_tip | 0.025 m (1 inch) | | Root diameter | d_root | 0.038 m (1.5 inch) | | Unsupported length | L | 0.15 m | | Thermowell material | - | 316 SS | | Modulus of elasticity | E | 193 GPa | | Material density | ρ_m | 8000 kg/m³ | Step 2: Calculate Reynolds Number [ Re = \frac\rho V d_tip\mu ] (μ = dynamic viscosity; for water at 20°C ≈ 1e-3 Pa·s) (simplified uniform beam): ( I = \frac\pi (d_root^4

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. thermocouple) from corrosive

[ St = \fracf_w \cdot dV ]

1. Introduction A thermowell is a pressure-tight receptacle inserted into a process pipe or vessel to protect a temperature sensor (e.g., RTD, thermocouple) from corrosive, high-pressure, or high-velocity fluids. When fluid flows past a thermowell, alternating vortices shed from its downstream side—a phenomenon known as vortex shedding or a Kármán vortex street .

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: