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What Is Fluid Mixing? Dimensionless Groups Reynolds Number Froude

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Agenda Fluid Mixing in Biotech and Pharmaceutical Applications • Mixing Theory What is Fluid Mixing? • Process Design of Agitators • Blending and Motion, Solids Suspension, Gas Dispersion • A combination of two or more species Kevin Eisert, Senior Application • Impellers -- Types and Styles Engineer through mechanical means to • Computational Fluid Mixing Susan Sargeant, Market Manager • Agitator Basics produce a desired result BPE • Gearbox/Agitator Types Eric Janz, Director-R&D • A rotating agitator produces high • Mounting Styles and Seals velocity liquid streams which come • Mechanical Design of Shafts into contact with stagnant or slower • Information Needed for Specifying an Agitator • Troubleshooting moving liquid, therefore momentum • Invited Comment transfer occurs. 1 2 3 Dimensionless Groups - Nomenclature Reynolds Number Dimensionless Groups • A measure of the ratio of inertial forces D = Impeller Diameter • Mathematical models obeying the (those produced by the agitator) to viscous T = Tank Diameter laws of conservation of mass and forces N = Impeller Rotational Speed 2 momentum yields a few significant •NRe = 10.7 N D Sg/: groups applicable to fluid motion Z = Liquid Level Height (: = cp, D = inches, N = rpm) • Will not derive the groups from the : = Fluid Viscosity • Affects: Navier-Stokes equation, rather they Sg = Fluid Specific Gravity • Power Draw of Impellers • Pumping Capacity of Impellers will be presented and significance C = Impeller Off Bottom Clearance • Static Mixer Design explained S = Impeller Spacing • Surface Deformation • Number of Impellers • Baffle Design 4 5 6 Power Number -vs- Reynolds Number Froude Number Power Number -- Np • A measure of the ratio of Inertial to • Dependent upon type/design of impeller and Gravitational Forces fluid properties •N= f ( N , N ) •N = N2 D/g = 7.2 x 10-7 N2 D p Re Fr Fr • Oftentimes N is not an effect and for high (N = rpm, D = inches) Fr NRe (Low Viscosity) the power number is • Used in Gas Dispersion and Solids Draw constant Down Applications • Experiments at different speeds, impeller • In many applications, gravitational effects are diameters, and fluid properties shows: unimportant and the Froude Number is not P % N3 P % D5 P % Sg significant • The ratio of Power to N,D, & Sg is the Power Number: 3 5 Np % P/(N D Sg) 7 8 9 1 What Affects Power Draw? Power Draw Calculation Pumping Number -- N • Fluid Properties such as Viscosity and q Specific Gravity and (if present) Gas • Dependent upon type/design of impeller • Impeller Type, Diameter, Pitch, and Width Hp = 6. 556 x 10-14 N3 D5 Sg Np and fluid properties • Impeller Rotational Speed • Flow of impeller is proportional to N & D3 • Geometric Effects such as Baffles, Coils, Q % N D3 Liquid Level, Pump Inlets, and Agitator Where: Mounting • The ratio of these two quantities is the N = Impeller Speed, rpm Pumping Number, Nq • Proximity Effects such as Impeller D = Impeller Diameter, inches 3 Nq = Q/ND Diameter to Tank Diameter Ratio and Off- Sg = Fluid Specific Gravity Q = N D3 N Bottom Clearance Np = Impeller Power Number q • Plus others to a lesser extent (blade •Nq = f (NRe) thickness) 10 11 12 Pumping Number -vs- Reynolds Number What Affects Pumping Rate? Pumping Rate Calculation • Fluid Properties: Viscosity, Presence of Gas, Specific Gravity -3 3 • Impeller Properties: Type of Impeller, Q (gpm) = 4.33 x 10 N D Nq Pitch, Width, Diameter, Clearance, etc. • Rotational Speed • Geometric Affects: Tank Diameter, Liquid Where: Levels, Draft Tubes, Baffles, etc. N = Impeller Rotation Speed, rpm D = Impeller Diameter, inches Nq = Impeller Pumping Number 13 14 15 Blend Time Blend Time Blend Time -- Turbulent Flow •Tb = F(NRe) •tu = -ln (1-U)/k Where: tu = Blend Time for “u” uniformity U = % uniformity k = Mixing Rate Constant, time –1 (See Advanced Liq. Agitation) • k = a N (D/T)b (T/Z)0.5 Where: a = Impeller Constant b = Impeller Constant N = Impeller Speed, rpm 16 17 18 2 Blend Time Blend Time What determines Agitator Size? • For 99% Uniformity • Blend times for higher viscosity fluids (NRe below turbulent) are corrected from a N • In simple terms, the size of the t99 = 4.605/k Re -vs- blend time chart agitator gearbox is rated on “Torque” Degree of Uniformity Relative Blend Time • Torque is proportional to Hp and 90 0.50 • Ways to improve Blend Time Speed 95 0.65 • Do not start from “Stratified” state 99 1.00 • Introduce additions near impeller J % Hp/N 99.9 1.50 • Pre-blend with Static Mixers (High Viscosity,Sg, • J (in-lbs.) = 63,025 Hp/N and Volume Ratios) 99.99 2.00 99.999 2.50 19 20 21 Torque Impellers Impeller Styles • 3 hp at 68 rpm Î 2,780 in-lbs. • 10 hp at 100 rpm Î 6,302 in-lbs. • Turbine Style Impellers • The 10 hp at 100 rpm, would be a size • Axial Flow (High Efficiency) “3” and the 3 hp at 68 rpm unit would be • Radial Flow (Straight Blade/Disc) a size “1” agitator • Close Clearance Impellers • Relative cost difference is about 40% • Helix/Anchor • For the same type impellers: • High Shear Higher Torque = Higher Flow = Higher • Rotor/Stator Cost 22 23 24 High Efficiency Impeller Commercial Impellers HE-3 Impeller Flow • Liquid Blending, Solids Suspension, Heat Transfer, • Following Impellers Show types of Upper Impeller in Gas Dispersion Impellers • Low Shear, High Pumping, Axial Flow • Reynolds Numbers $100 • Examples of the impellers are from • Turbulent Np = 0.28 (0.26 - 0.30) Chemineer • For a given agitator, the appropriate HE impeller is 20 percent larger than a pitched blade • Other Manufacturers Manufacture • Jet Foil Impellers will adhere to similar characteristics similar impeller styles HE-3 Impeller 25 26 27 3 High Efficiency/Hydrofoil Impeller High Efficiency High Solidity Impeller Np = 0.85 (0.8 to 0.95) •Liquid Blending, Heat Transfer, Solids Suspension •Low Shear, Axial Flow, High Pumping • Wide Blade hydrofoil impeller, axial flow •Similar in performance to HE-3 • Applications which require a high solidity axial •Np = 0.55 (0.5 to 0.6) flow impeller: three-phase systems, gas •Curved design of blade/hub results in higher strength: dispersion, abrasive solids, transitional flow lower weight (100>Nre<2,000) •Design requires cast impeller hubs SC-3 Impeller Maxflo W 28 29 30 Pitched Plade Impeller P-4 Impeller Flow Straight Blade Impeller • Liquid Blending, Heat Transfer, Solids Suspension • Straight Blade Impeller with four blades • Especially good for drawing a vortex or for • Liquid blending, keep outlets clear from solids, material drawdown solids drawdown, tickler@ impeller, immiscible • Mixed Axial/Radial Flow fluid blending • Typical: 4-Blades, W/D = 0.20, 45 degree • Reynolds Number >1 • Turbulent Np = 1.3 (1.15 - 1.45) • Turbulent Np = 2.88 • Reynolds Number >10 • Simple flat blade design is often economical P-4 Impeller S-4 Impeller 31 32 33 Rushton Turbine High Efficiency Gas Dispersion Impellers Gassed Power Draw Comparison • 6-Bladed Disc Style Impeller • 6-Bladed Curved Disc Impeller • Gas dispersion at low and intermediate • Gas Dispersion at all gas rates gas rates, liquid-liquid dispersion • Fermentations, Liquid/Liquid Dispersions • Turbulent Np = 5.0 CD-6 BT-6 • Dated Technology D-6 Impeller 34 35 36 4 Helical Ribbon Mass Transfer Coefficient Anchor Impeller 0.3 BT-6 • Close Clearance Agitator • Close Clearance Agitator 0.25 • Typical D/T Range: 0.95 - 0.98 • Typical D/T range: 0.95 - 0.98 CD-6 0.2 • Viscous Liquids (> 100,000 cp) • Viscous Liquids (> 100,000 cp) 0.15 • Blending and Heat Transfer • Blending and Heat Transfer D-6 • Less efficient but more cost effective than 0.1 Helical Ribbon Mass Transfer Coefficient (1/s) 0.05 • Less surface area for cleaning than Helical Ribbon 0 0 0.02 0.04 0.06 0.08 0.1 Superficial Gas Velocity (m/s) 3 Retrofit comparison kla at Pu/V = 2.2 kW/m 37 38 39 Choosing Impellers Impeller Performance - Example •Flow Controlled Processes: High Pumping/Low Shear System Geometry and Impellers •Blending Miscible Fluids, Heat Transfer, Solids Susp. HE-3 •High Efficiency/Pitched Blade/High Solidity JF3 •Dispersion Processes SC-3 •Gas Dispersion, Immiscible Fluids Maxflo W ® Impeller System •Radial Flow Impellers P-4 •Combination: Lower Radial (Disk)/Upper Axial S-4 BT-6 ® Baffle Recommendations CD-6 D-6 Rotor/Stator Low Pumping/High Shear 40 41 42 Impeller Performance Geometry Impeller Design Options •Buffer Tanks, Blend Tanks, Heat Transfer, Solids Susp. • All welded impellers • Number of impellers depends on • Type of impeller • High Efficiency Impellers • Threaded/sealed impellers • Reactors: • Viscosity/Reynolds Number of fluid • High Efficiency Impellers • Bolted (acorn nuts) blades • Liquid Level to Tank Diameter Ratio (Z/T) • Gas Dispersion Impellers • Set Screws, Keys, other options available • Impeller Diameter/Tank Diameter (D/T Ratio): • Pitched Blade Impellers • Affects Power Number of Impeller • Helix (High Viscosity) • Large D/T ratios not advised for Solids Susp. • Solids Drawdown • Location • Pitched Blade Impellers • For low level mixing, “tickler” impeller used 43 44 45 5 Baffles Recommended Baffling Impeller Equations •Primary Pumping Capacity • Baffles are used to prevent swirling in lower viscosity Reynolds • Q (gpm) = 4.33 x 10-3 N D3 Nq applications and promote Atop to bottom@ mixing. Number Baffles • Impeller Horsepower Draw • Baffled Tanks produce the best mixing results •P = 6.556 x 10-14 N3 D5 Sg Np NRe > 1,000 T/12 width, T/72 offset • Impeller Reynold’s Number 500 < NRe < 1,000 T/24 width • Baffling not required in angled or vertical off center mixing 2 •NRe = 10.7 N D Sg / : NRe < 500 None • In certain
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