อัปเดต 2026-09-07

Gas-Liquid Agitator

Rushton aerated stirred tank

Sizes an aerated stirred-tank agitator (Rushton/CD-6/pitched-blade/hydrofoil impellers): ungassed and gassed power draw, flooding/loading/complete-dispersion regime, kLa mass-transfer duty, gas hold-up, motor/torque sizing, and sparger (ring-orifice or porous) geometry.

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Computes the dimensionless groups (Re, aeration number Na, Froude) from geometry and operating speed, applies the Rushton power-number correlation for ungassed power and the Michel & Miller (1962) correlation for gassed power, locates the dispersion regime via Nienow's Na_F/Na_CD transition numbers, then evaluates the Van't Riet (1979) kLa correlation and a Calderbank-style gas hold-up fit. Motor is sized on the ungassed (gas-trip) power with a 15% service factor.

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Ungassed & gassed power (Rushton / Michel-Miller)

P_{0} = N_{p} ρ N^{3} D^{5} P_{g} = 0.706 [\frac{P _{0}^{2} N D ^{3}}{Q _{g}^{0.56}}]^{0.45}

N_p = 5.0 for a 6-blade Rushton disc turbine, fully turbulent (Re > 1e4); Michel & Miller, AIChE J. 1962, SI form with Q_g in m³/s.

Reynolds, aeration & Froude numbers

R e = \frac{ρ N D ^{2}}{μ} N a = \frac{Q _{g}}{N D ^{3}} F r = \frac{N ^{2} D}{g}

N in rev/s, g = 9.80665 m/s². Na compared against Nienow's transition numbers Na_F ≈ 30(D/T)^3.5·Fr and Na_CD ≈ 0.2(D/T)^0.5·Fr^0.5 sets the flooding / loading / complete-dispersion regime.

Volumetric mass-transfer coefficient (Van't Riet 1979)

k_{L} a = 0.026 (\frac{P _{g}}{V})^{0.4} U_{s g}^{0.5} (coalescing, water-like)

Non-coalescing/electrolyte form: k_L a = 0.002·(P_g/V)^0.7·U_sg^0.2 [s⁻¹]. P_g/V in W/m³, superficial gas velocity U_sg = Q_g/(π/4·T²) in m/s. Ind. Eng. Chem. Process Des. Dev. 1979, 18(3):357–364.

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