agitator-design

name	agitator-design
description	Agitator/mixer design — impeller type selection, Power number/Flow number, Reynolds number for mixing, blend time, gas-liquid mixing, scale-up, baffles, ASME mixing vessel, Rushton turbine, pitched blade.
metadata	{"priority":7,"promptSignals":{"phrases":["agitator design","mixer design","impeller selection","Power number mixing","blend time","mixing tank design","Rushton turbine"],"minScore":3}}

Agitator/Mixer Design — Complete Skill

Impeller Types and Selection

Impeller	Flow pattern	Np (turbulent)	Nq	Best use
Rushton disc turbine (RT)	Radial	5.0	0.72	Gas-liquid; high shear
Pitched blade turbine (PBT)	Axial/radial mix	1.5–2.0	0.87	Blending; solids suspension
Hydrofoil (HE-3, A310)	Axial	0.3–0.6	0.55	Blending; low viscosity
Anchor	Tangential	0.4–1.0	—	High viscosity (Re < 100)
Helical ribbon	Axial	300/Re	—	Very high viscosity
Marine propeller	Axial	0.3	0.5	Low viscosity; bulk mixing

Dimensionless Numbers

Reynolds number for mixing: Re_mix = ρ × N × D² / μ N = rotational speed [rev/s]; D = impeller diameter [m]; ρ = fluid density [kg/m³]; μ = dynamic viscosity [Pa·s]

Turbulent: Re > 10,000 (Np = constant) Transitional: 10 < Re < 10,000 Laminar: Re < 10 (Np = K_p/Re; K_p depends on impeller)

Power number Np: P = Np × ρ × N³ × D⁵ [W; P = agitator shaft power] Np from impeller data at given Re and baffle configuration

Flow number Nq: Q_pumped = Nq × N × D³ [m³/s; impeller pumping rate]

Blend number Nθ (blending): t_blend = Nθ / N [s; Nθ typically 30–60 for turbulent mixing]

Tank Geometry and Baffles

Standard geometry ratios: T = tank diameter; H = liquid height; D = impeller diameter H/T = 1.0 (standard); D/T = 0.3–0.4 (turbines); D/T = 0.5–0.6 (hydrofoil low power) Bottom clearance: C = T/4 to T/3

Baffles: Standard: 4 baffles; width W_b = T/12 to T/10; installed vertical, near wall Without baffles: swirling vortex; poor mixing; power draw lower With baffles: turbulent; Np = full (Table above)

Multiple impellers: For H/T > 1.2: add second (upper) impeller Impeller spacing: S = 0.8–1.2 D between impellers

Power Calculation

Agitator power: P = Np × ρ × N³ × D⁵ [W]

Motor power: P_motor = P / (η_motor × η_gearbox) × service_factor η_motor = 0.92–0.96; η_gearbox = 0.94–0.97; service factor = 1.25

Example — Rushton turbine: D = 0.5 m; N = 3 rev/s; ρ = 1000 kg/m³; Np = 5.0 (turbulent) P = 5.0 × 1000 × 3³ × 0.5⁵ = 5.0 × 1000 × 27 × 0.03125 = 4219 W ≈ 4.2 kW

Blend Time Correlations

Turbulent blend time (Nienow, Ruszkowski): t_mix = (T/D)^2.43 × (T/H)^0.5 × (5.9/N) × (T/D) [simplified; check specific correlation]

More accurate (Grenville & Nienow 2004): N × t_blend = C₁ × (T/D)^α × (H/T)^β [correlation constants from literature]

Conservative estimate: t_blend = (4–5) × circulation_time = (4–5) × V_tank / Q_pumped

For blending miscible liquids: t_blend (95% uniformity) ≈ 20–30 circulation times (laminar); 5–10 (turbulent)

Gas-Liquid Mixing

Gas dispersion power: P_gassed / P_ungassed = f(FlG) [gassed power fraction depends on gas flow number] Gas flow number: FlG = Q_gas / (N × D³) [Q_gas = volumetric gas flow at tank conditions]

Nienow correlation: P_g/P = 0.1 × (N² D³ / (g × V_L^(1/3) × Q_g^(2/3)))^(-0.5) [approximation; use chart for accuracy] For Rushton: P_g/P ≈ 0.5 at FlG = 0.04

Superficial gas velocity: U_g = Q_gas / A_tank [m/s] Minimum for gas distribution: U_g ≥ 0.01–0.02 m/s

Flooding (gas not dispersed): Flooding FlG > FlG_flood = 30/(Np)^0.5 × (D/T)^3.5 [at flooding; impeller overwhelmed]

k_L a (volumetric mass transfer coefficient): k_L a = C × (P_g/V_L)^α × U_g^β C, α, β from Higbie penetration theory or empirical (Van't Riet correlation): k_L a = 0.026 × (P_g/V_L)^0.4 × U_g^0.5 [s⁻¹; P_g/V_L in W/m³; U_g in m/s]

Solids Suspension

Zwietering correlation (just-suspended speed N_JS): N_JS = S × ν^0.1 × d_p^0.2 × [(g(ρ_s - ρ_L)/ρ_L)^0.45] × (C_s/D)^0.13 / D^0.85 S = Zwietering parameter (from impeller/geometry table; 4–8 for turbines) ν = kinematic viscosity [m²/s]; d_p = particle diameter [m]; C_s = solids loading [kg_solid/m³_liquid]

Rule: design for 1.1–1.2 × N_JS to ensure all solids in suspension

Scale-Up Criteria

Equal power per unit volume (P/V = const): N_scale = N_lab × (D_lab/D_scale)^(2/3) [most common for mixing] P/V constant; blend time increases with scale (t_blend ∝ D^(2/3))

Equal tip speed (V_tip = π N D = const): N_scale = N_lab × (D_lab/D_scale) Better for shear-sensitive processes (cells, crystals)

Equal blend time: N_scale = N_lab → P/V increases (expensive at scale)

Equal Froude number (surface behavior): Fr = N² D / g = const → N ∝ D^(-0.5) Use for surface aeration or vortex formation

Output

Provide: impeller type, diameter D [m] and T/D ratio, speed N [RPM], Power number Np, shaft power P [kW] and motor power [kW], pumping rate Q [m³/s], blend time t_blend [s], gas flow number FlG (if gas-liquid), k_L a [s⁻¹] (if mass transfer), just-suspended speed N_JS [RPM] (if solids), baffle specification, scale-up basis and governing criterion, and applicable reference (ASME mixing design guides; Handbook of Industrial Mixing).