Kutateladze Number (Ku) Formula: Countercurrent Gas-Liquid Flooding & Droplet Entrainment

When pipe diameter exceeds ~30 Capillary Lengths, Wallis fails and Kutateladze Ku_crit ≈ 3.2 governs flooding!

In small-bore vertical tubes, countercurrent gas-liquid flooding scales with pipe diameter D via the Wallis parameter j_g*. However, Samson Semenovich Kutateladze (1948–1972) and Pushkina & Sorokin (1969) proved that once hydraulic diameter exceeds ~30–40 Laplace capillary lengths L_cap = SQRT(sigma / (g * (rho_l - rho_g))) (~80–100 mm for air-water), interfacial Taylor-wavelength instabilities decouple from pipe wall diameter altogether!

Replacing pipe diameter D with the Laplace capillary length yields the dimensionless Kutateladze gas number: Ku_g = j_g * SQRT(rho_g) / (9.81 * sigma * (rho_l - rho_g))^0.25! In vertical countercurrent channels, onset of liquid droplet entrainment begins near Ku_g ≈ 0.2–0.5 and complete zero-liquid-penetration flooding occurs at Ku_g >= 3.2! For air-water (rho_g = 1.25 kg/m^3, rho_l = 996 kg/m^3, sigma = 0.072 N/m), superficial gas velocity j_g = 0.85 m/s gives Ku_g = 0.1846 (rising to 0.5212 at j_g = 2.40 m/s)!

Dimensionless Kutateladze Gas Flux Number Ku_g = j_g * SQRT(rho_g) / (9.81 * sigma * (rho_l - rho_g))^0.25

Evaluates Ku_g from superficial gas velocity j_g (B2, m/s), gas density rho_g (B3, kg/m³), liquid density rho_l (B4, kg/m³), and surface tension sigma (B5, N/m).

=IF(OR(B2 < 0, B3 <= 0, B4 <= B3, B5 <= 0), "Invalid Two-Phase Properties", ROUND(B2 * SQRT(B3) / ((9.81 * B5 * (B4 - B3)) ^ 0.25), 4))

Pushkina-Sorokin Large-Diameter Countercurrent Flooding Check (Ku_g >= 3.2)

Tests whether Ku_g exceeds the critical zero-penetration flooding threshold Ku_crit = 3.2.

=IF(OR(B2 < 0, B3 <= 0, B4 <= B3, B5 <= 0), "Invalid Two-Phase Properties", IF(B2 * SQRT(B3) / ((9.81 * B5 * (B4 - B3)) ^ 0.25) >= 3.2, "Countercurrent Flooding (Ku >= 3.2 — Zero Liquid Penetration)", "Below Complete Flooding Limit (Ku < 3.2)"))

Further reading

• Microsoft Support — SQRT function