Agitation and Mixing

Agitation and mixing

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Agitation vs. Mixing Agitation – induced motion of a material in a specified way – Usually a circulatory pattern inside a container

Mixing – random distribution, into and through one another, of two or more initially separate phases – Various degrees of homogeneity

Applications

Introduction

(1) dispersion of solvable solid (2) homogenization of miscible liquids (3) mixing and dispersion of immiscible liquids (4) mixing between gas and liquid (5) suspension of solid particles in liquid (6) acceleration of chemical reaction and physical transport

Agitation methods mechanical agitators gas agitation jet mixing static mixer tubular mixing

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Agitation Equipment T-Junctions Static Mixers Tank or vessel – Cylindrical in form with a vertical axis – Rounded or flatten tank bottom – Depth  diameter

Impellers – Axial-flow – generate currents parallel with the axis of the impeller shaft – Radial-flow – generate currents in a tangential or radial direction – Propellers, paddles, and turbines

Motionless mixers

T-junction (similar flow rates)

Perforated plates (orifices) supported on a rod

Pitot tube (different flow rates)

Flanged perforated plates

Injector mixer with a helical baffle Hellical mixing elements with alternating directions (Kenics)

Kenics Static mixers

Komax static mixer

Pump recirculated tank(homogenizer)

Mechanically agitated mixing equipment A set of mixing equipment consists of: a mixing tank a driving motor with speed reducer an agitator some attached parts. Agitator is the main part, like an impeller in a pump to give mechanical energy to liquid. 9

Types of agitators – axial type propeller standard type： S/d=1，Z=3 blade end speed: 5~15 m/s, maximum 25 m/s helical ribbon Standard type： S/d=1, B/d=0.1 Z=1-2 (2 for twin ribbon type) low speed, the outer edge is very close to the tank wall (close clearance impeller).

10

Types of agitators – radial type blades standard type d/B=4-10，Z=2 blade end speed 1.5~3 m/s anchor and frame standard type： B/d=1/12 d’/d=0.05-0.08, d’=25-50 mm d’- distance between the tank wall and the outer edge of the anchor blade end speed 0.5-1.5 m/s 11

Propellers Propellers – axial-flow, high speed impeller for liquids of low viscosity – Small – 1150-1750 r/min – Large – 400-800 r/min – Pitch – ratio of movement of liquid over fixed distance to propeller diameter – Standard – 3-blade marine propeller with square pitch (1.0) – Rarely exceed 18” in diameter

Paddles Two or four blades turning on a vertical shaft – – – – –

Simple mixing problems 20-150 r/min Length usually 50-80% of inside diameter Width is 1/6th to 1/10th of length Use with baffles at high speed to achieve good mixing

Turbines Multi-bladed paddle agitators with short blades – Turn at high speed on centrally-mounted shaft – Smaller diameter; 30-50% of diameter of vessel – Effective over wide range of viscosities

Types of agitators – radial type

turbines

straight blades on disk (Rushton) curve blades on disk

open straight blades (paddle) open curve blades 15

Agitator types

Concave-blade CD-6 impeller

3-blade marine propeller

Pitched-blade turbine

Simple straight-blade turbine Disk turbine

(paddle)

Agitator types

three-bladed mixing propeller

Turbine with inclined blades (usually45°)

turbine with flat vertical blades

Curved blade turbine

Flat blades disk turbine (more blades)

Shrouded turbine (consisting of a rotor and a stator)

Agitator types Cage beater impeller (usually mounted on the same shaft with a standard propeller)

Anchor paddle Sawtooth edges flat plate turbine

Hollow shaft and hollow impeller assembly Gate paddle

shrouded screw impeller and heat exchange coil

Special mixers for powders and pastes

Ribbon blender for powders

Twin shell (Vee type)

double cone blender

Twin rotor

Special mixers for powders and pastes

Batch muller

Double-arm mixer and kneader

Twin mullers

Some types of blades for the double-arm kneader

Flow Patterns Depends on type of impeller, characteristics of fluid, size and proportions of tank, baffles, and agitator Swirling – stratification at various levels with no longitudinal flow between levels

Types of agitators It can be divided by flow pattern axial-flow The main flow in tank is a circulation on axial direction (& tangential) with little turbulent. Suitable for mixing of low viscose liquids, particle suspension and heat transfer enhance. Propeller small diameter, high speed, large flow rate and low head. Helical ribbon large diameter and mixing range, low speed, 22 low head. Special design for high viscosity liquid.

Types of agitators Radial-flow Complicated radial and tangential flow. For low & middle viscosity liquids in dispersion of immiscible liquids, chemical reaction and heat transfer. turbines: high speed，wide blade，low flow rate and high head. straight blades: long vane, low speed and low head, for high viscosity liquids. anchor and frame ：very large diameter and mixing range, very low speed and head. Suitable for high viscosity liquids and capable of preventing the deposit on tank wall. 23

Baffle and draft tube tangential vortex- by centrifugal force. The liquid level on tank center will fall to form a forced vortex. The high the speed , the deep the vortex. result effective volume reduced and mixing effect worsen. Sometimes gas is absorbed from lower liquid level to disturb operation.

Solution 1 install baffles on tank wall. Maximum 8 baffles (usually 4), called “fully baffled” 24

Baffles and draft tube Solution 2 off-central installed agitator will improve the operation with increased power consumption. draft tube mixing through controlling the flow velocity and direction, reducing the short cut. Especially for particle suspension.

Side entering impellers

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Large tanks agitation: side entering impellers

Vortex inhibition: off-centering & baffles

Axial or radial impellers without baffles produce vortexes

Off-center located impellers reduces the vortex

Lateral baffles reduces the vortex

Flow patterns: radial vs axial impellers

Radial impeller

Axial impeller

Multiple-impeller tank

Standard dimensions

Standard geometry w 4 baffles

D=

T/2;T/3

H=

T

a=

D/4

b=

D/5

c=

T/2;T/3

d=

0.75D

w

T/10

d

H a c

T

D b

Circulation, Velocities, and Power Consumption Volume of fluid circulated by impeller must be sufficient to sweep out entire vessel in reasonable time Velocity of stream leaving impeller must be sufficient to carry current to remotest parts of tank In mixing, also it needs turbulence

– Results from properly directed currents and large velocity gradients in liquid

Circulation and generation of turbulence both consume energy Large impeller + medium speed = flow Small impeller + high speed = turbulence

Flow pattern in mixing tank Flow pattern is related with the geometries of tank, stirrer and baffle, liquid properties and stirrer speed. For agitation operation, the useful flows are axial and radial, not the tangential. rotating speed, rps Stirring Re

Re  D 2 N  / 

DN = u

Tip speed

For a fully baffled standard tank with an 6 straight blades turbine, the following flow regimes hold: 1＜ Re＜10 near the turbine: laminar flow, other zones: almost static Re＞10

laminar axis flow, flow starts from blade’s tips

100＜Re103

turbulent in whole tank

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Mixing mechanism (1) molecular diffusion：occurring in molecular scale (2)turbulent diffusion ： caused by vortex dissipation, existed in vortex size . (3)convective diffusion：caused by convection, occurring in large scale spaces. Convective flow breaks the liquid into large drops (macro mixing); the drops are then broken into smaller ones by vortex deformation (inter-drop mixing) ； those vortex breakage and deformation will increase or renew the contacting area between drops with different concentration and promote the molecular diffusion. A fully homogeneous mixing depends on molecular diffusion. In comparison, the turbulent diffusion is about 105~107 times of molecular diffusion and dominates the turbulent agitation. 33

Mixing sensitive processes Considering that a mixer consumes (depending on its shape, dimension and agitation speed) a determined amount of mechanical power, it can be dissipated inside the vessel by inducing large flow rates (bulk motion) or high levels of turbulence due to liquid shear (shear stresses). Typically, axial impellers promote bulk motion while radial ones promote instead shear stresses. Processes promoted by mixing may be classified on the basis of their sensitivity to bulk motion or shear stress promotion: Bulk motion controlled processes – those which do not need to create new interface (blending, heat transfer promotion) or which must allow the availability of the actual interface for exchange processes (solid suspension). Shear rate controlled processes – those which efficiency rely on the generation of inter-phase exchange surface (gasliquid and liquid-liquid dispersions).

Mixing mechanism of homogeneous systems low viscosity liquids Large vortex is broken into small ones by shearing effect. The viscose resistance converts part of the mixing energy into heat. Strong mixing effect occurs at the zone near the agitator. Total circulation flow rate is the most important for this type of mixing. high viscosity liquids In the laminar zone, mixing depends on the total flow. But the agitator efficiency is low at turbulent zone. Large diameter (often “close-clearance”) and low speed agitators should be used. Impeller must sweep the whole 35 vessel volume to assure good mixing.

Mixing mechanism of heterogeneous system Immiscible liquid-liquid systems One phase is continuous and another is dispersed. For zone near the agitator, the shearing effect is strong under high turbulent and small liquid drops will be achieved. In the zone far away from the agitator, the drops will agglomerate into larger ones. The breakage and agglomeration processes increase and renew the interface of the liquids, so strengthen the inter-phase mass transfer. If a surface activation agent is added in this system, the agglomeration will be weaken and the size of liquid drops tends to be uniform. 36

Mixing mechanism of heterogeneous systems gas-liquid systems The mechanism is similar to the liquid-liquid systems. Gas is dispersed as bubbles in the liquid . Gas-liquid interface tension is stronger than that of liquidliquid and the dispersion of gas is more difficult. As a result, the sizes of bubbles are larger than those of liquid drops. The large density difference between gas and liquid makes the gas bubbles rise to the top of the liquid. High shearing agitators are often used to generate relative small gas bubbles (radial types are preferable). 37

Mixing mechanism of heterogeneous system solid-liquid systems The purpose of the agitation are • to suspend the particles homogeneously in the liquid • to reduce the thickness of liquid film on particle surface in order to accelerate the reaction or transport processes. Critical speed for suspension

(Njs)

It is minimum rotating speed needed to suspend all particles. It depends on the agitator size and type as well as on the physical properties of suspension. 38

Why Dimensionless Numbers? Empirical correlations to estimate the power required to rotate a given impeller at a given speed, with respect to other variables in system: – – – – –

Measurements of tank and impeller Distance of impeller from tank floor Liquid depth Dimensions of baffles Viscosity, density, speed

Dimensional analysis for fluid agitation systems Basic quantities Characteristic length:

Impeller diameter

Characteristic time:

Inverse impeller speed: 1/N (s)

Characteristic mass:

Liquid density and cube of impeller diameter:

D (m)

 D3 (kg)

Derived quantities Characteristic velocity: Impeller diameter and speed: DN (m/s) Characteristic pressure: Density and velocity square: Characteristic flow rate: Velocity and area

 D 2 N 2 (Pa) ND3  m3 /s 

Dimensionless numbers Reynolds N Re =

N D2 



Qi Pumping (Flow) N Q = ND3

Weber

N We =

N 2 D3 



Wbrake N 3 D5 

;

Power N Po =

;

N2D Froude N Fr = g

Dimensionless Mixing Numbers Flow rates pumped by the impeller pumping flow rate Q： flow rate pumped through a “reference” surface of the agitator

Pumping Number NQ=Q/ND3 Where Q is the volumetric flow rate, measured over a fixed control surface (depending on the agitator type), N is the rotational speed (rps), D is the impeller diameter.

For turbulent flow, NQ is a constant, not a function of Re

Q  ND

3

Typical NQ values:

Standard flat-blade turbine, NQ = 1.3

Marine propellers, NQ = 0.5-0.9 (dep. on pitch) 4-blade 45 turbine, NQ = 0.5

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Pumping number

Axial impellers

q

q

Radial impellers

Dimensionless Mixing parameters Flow rates pumped by impeller Total circulating flow rate Q’ : all circulating flow rate in the tank by the entrainment from the agitator，Q’ > Q.

Circulating flow rate number NQ’ = Q’/ND3

(Re>103)

For turbulent flow & standard geometry:

N Q'

  D  2    N Q 1  0.16   1    d   

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Dimensionless Mixing parameters Mechanical power required by impeller P The power P dissipated divided by N3D5 corresponds to an important dimensionless parameter of mixers, the Power Number NP:

Power Number NP=P/N3D5 Where P is the mechanical power dissipated (watts), measured at the tip of the blades, N is the rotational speed (rps), D is the impeller diameter and  is the fluid density.

NP is ratio of drag force to momentum flow, NP is analogous to the friction factor f for CD . Typical values: Standard flat-blade turbine, baffled vessels NP = 5 Standard flat-blade turbine, unbaffled vessels NP = 1 Marine propellers, NP = 1

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Calculation of Power Consumption P  NP N D  3

5

At low Re (10 000 in baffled tanks, P is independent of Reynolds Number and viscosity is not a factor:

N P  KT

P  KT N 3 D 5 

KL and KT are constants for various types of impellers and tanks Please note the dependency of P on  or  depending on the flow regime (laminar or turbulent).

Power constants at low (KL) and high (KT) Reynolds number Type of Impeller

KL

KT

41 55

0.32 0.87

65 70 44.5

5.75 4.80 1.63 1.27

Flat paddle, 2 blades (45, S4=0.2)

36.5

1.70

Anchor

300

0.35

Propeller, 3 blades Pitch 1.0 Pitch 1.5 Turbine 6-blade disk (S3=0.25 S4=0.2) 6 curved blades (S4=0.2) 6 pitched blades (45, S4=0.2) 4 pitched blades (45, S4=0.2)

Correlations and power curves For a complicated mixing process, dimensional analysis is often used to correlate the experimental data and find the empirical Eqs. With a standard mixing unit, following results can be found from the dimensional analysis Pw  f  N , D,  ,  , g 

 ND 2  N 2 D  Pw  f , NP   N P  f  Re, Fr  3 5 N D  g  

NP —— power number

Re —— stirring Reynolds number for flow pattern Fr —— Froude number for circulating flow with free surface 48

NP vs Re for different turbines

Power number NP vs. Re: baffled & unbaffled tanks (marine propellers and helical ribbons)

propellers baffled

unbaffled

Helical ribbon unbaffled

helical ribbons

NP vs Re for propellers

NP vs Re for different impellers

Effects of D/T for two axial flow impellers

Decreasing D/T ratio

NQ vs Re (Pitched-blade turbine)

Mixing processes: blending Blending is the mixing operation aimed to homogenise two or more miscible liquids by agitation. The blending efficiency depends on the global flow rate moved by the impeller (bulk motion controlled process). The residence time required to achieve complete homogenization of inlet flow rate is called “mixing time” (tT). For non viscous liquids it is commonly assumed that the mixing time correspond to the time required by the impeller to recirculate 5 times the whole tank content. 5V 5 T H const  T  tT      3 Q ' 4 N Q ' ND NQ ' N  D  2

NQ’ = circulating flow rate number N = rotational speed, rps T = tank diameter, m H = liquid height, m

2

const  T    NtT  NQ '  D 

2

Blending time vs Re

Mixing time correlations For standard Rushton turbine (fully turbulent regime) the total flow rate circulated by the impeller is Q’=0.92ND2T , it follows:

5V 5 T 3 4.3  T  tT      2 Q ' 4  0.92 ND T N D

2

T  NtT  4.3    D

2

Mixing time factor

tT = mixing time, s N = rotational speed, rps T = tank diameter, m H = liquid height, m

For HE-3 high-efficiency impeller (fully turbulent regime) the mixing time factor is: 1.67

T  NtT  16.9    D

H   T 

0.5

Mixing time correlations For standard Rushton turbine (fully turbulent regime) the total flow rate circulated by the impeller is Q’=0.92ND2T , it follows:

5V 5 T 3 4.3  T  tT      2 Q ' 4  0.92 ND T N D tT = mixing time, s V = liquid volume, m3 N = rotational speed, rps D = impeller diameter, m T = tank diameter, m H = liquid height, m

2

T  NtT  4.3    D

2

Mixing time factor

Mixing Time factor correlations For Rushton turbine (fully turbulent regime) the mixing time factor is:the 1/Fr 2

1/2

1/6

tT ( ND 2 ) 2/3 g 1/6 D1/2 D  T   g  ft  Nt  T      2  H 1/2T 3/ 2 T  H  N D

When Re>105, ft  5

For HE-3 high-efficiency impeller (fully turbulent regime) the mixing time factor is: 1.67

T  NtT  16.9    D

H   T 

0.5

Mixing time factors in agitated vessels

Dashed lines: unbaffled tanks

Solid lines: baffled tanks

Dimensionless parameter dependency on Re summary

Solid particle suspension Processes involving solid particle suspension in liquids (leaching, solid catalysed reactions, crystallization, ...) are often carried out in agitated systems. The role of agitation is to made available to mass and heat exchange all the solid surface, therefore all particle should move freely inside the tank. This is a bulk motion controlled process. Aim of agitation: • Produce a homogeneous mixture • Dissolve solids • Catalyze a chemical reaction • Promote growth of a crystalline product from a supersaturated solution

Solid particle suspension regimes Four different regimes apply for solid suspension: 1) Incomplete suspension: all or part of particle rest at the bottom tank, forming “fillets”. This regime may be acceptable only if the amount of unsuspended particles is small; 2) On-bottom suspension: particles are suspended or, at least, move on bottom. 3) Off-bottom suspension: all particles do not rest at bottom for more than 1-2 seconds (Just Suspension regime). This a commonly adopted working regime of suspension; 4) Homogeneous suspension: particles are uniformly distributed inside the whole tank (particle concentration is almost constant). It is a high power requiring regime and it is impossible to achieve for heavy particles. It is needed for very special applications.

Solid particle suspension The most used correlation to estimate the Just Suspension agitation speed (NJS) is that proposed by Zwietering:

N JS  S d 0.1

0.2 p

   g   L  

0.45

D 0.85 B 0.13

NJS= just suspension speed, rps S= geometry factor, = kinematic viscosity, m2/s dp= particle diameter, m g = gravitational acceleration, m/s2  = particle to liquid density difference, kg/m3 L = liquid density , kg/m3 D = impeller diameter, m B = particle mass to liquid mass ratio x 100, %

Dimensional correlation!

Shape Factor, S Impeller type

T/D

T/E

S

(E is height of impeller above vessel floor)

6-blade turbine D/W = 5 NP = 6.2

2 3 4

4 4 4

4.1 7.5 11.5

2-blade paddle D/W = 4 NP = 2.5

2 3 4

4 4 4

4.8 8 12.5

3-blade propeller NP = 0.5

3 4 4

4 4 2.5

6.5 8.5 9.5

For the same geometry, critical speed is about the same for standard turbine and paddle However, turbine requires twice as much power as paddle, and 15-20 times as much power as propeller Sole purpose to suspend solids – use propeller For good gas dispersion or high shear – use turbine

Power required for complete suspension of solids in agitated tanks using pitched-blade turbines

Gas-Liquid dispersions Gas liquid mechanically agitated systems are used for those processes where a gas-liquid mass transfer phenomena are involved (hydrogenation, chlorination, oxidation, ...). The role of mixing is to: • generate as much interfacial area as possible (by disrupting the gas phase) • disperse the bubbles throughout the liquid • keep the bubbles in the liquid (i.e. recirculate) for sufficient time • homogenize the liquid concentration • enhance mass and heat transfer coefficients. To this aim, impellers that produce large shear stresses (high velocity turbines) are preferable.

Gas-Liquid dispersions The gas phase is fed on the lower part of the tank, below the impeller, through a gas sparger. Gas spargers may consist simply of open end tubes or may be slightly more complicated (perforated rings, porous plates). The importance of gas sparger is not as crucial as in other non agitated systems (e.g. bubble columns) as the gas phase dispersion is mainly performed by the impeller. sparger

Gas-Liquid dispersions regimes Depending on the agitation speed N and the gas flow rate QG different dispersion regimes hold: Surface aeration

(open systems)

a) & b) Flooding

Loading

Complete dispersion

Highly gas recirculation regime

Gas-Liquid dispersions regimes

Correlation to regime transition parameters estimation: 2 QG  D   NF D  D   Fl  30 30  F      FrF N F D3 T g    T   3.5

Flooding  Loading (NF) Loading  Compl. Disp. (NCD)

3.5

2 QG  D   N CD D   0.2     3 N CD D T   g 

Compl. Disp. High Gas Rec. (NR)

0.5

0.5

 FlCD 2

D  0.2   T 

0.5 0.5 FrCD

2 QG  D   NR D  D 2  13  Fl  13  R      FrR 3 NR D T   g  T  5

5

Gas-Liquid power requirements The gas strongly affects the fluid dynamics inside the tank as it interferes in the impeller momentum transfer. Therefore correlations of NP valid for single phase do not hold anymore. The figure shows how the ratio of power in gassed conditions (Pg) over the power consumed in ungassed systems (P) varies with the Flow Number (Fl) at constant gas flow rate QG:

Pg/P always < 1

Power curves at constant gas rate for Rushton turbines.

Gas cavities behind blades

disc

Increasing agitation speed

Gas-liquid dispersion empirical correlations Michel & Miller correlation to predict Pg in standard systems:

 P ND  Pg    0.56   QG  2

3

m

Dimensional correlation (SI units required) P=ungassed power requirement [W], Pg [W] N [rps], D [m], QG [m3/s] = 0.83 (Rushton turbine, standard geometry) m=0.45 normally coalescent liquids

Van’t Riet correlation to calculate the volumetric gas-liquid mass transfer coefficient (kLa) in standard systems: 

 Pg   k L a     vsg  VL 

Dimensional correlation (SI units required): Pg [W], VL [m3] liquid volume kLa [1/s], vsg superficial gas velocity (Qg/Stank) [m/s]   

Coalescent systems 0.026 0.4 0.5

Non coalescent systems 0.002 0.7 0.2

Pg/P vs QG for different impellers

Pg/P always < 1

Typical power curves for gassed agitators (D.T.= disc turbine; V.D.= vaned disc; P.B.T. = pitched blade turbine. All curves for one N and D.)

Liquid-liquid dispersions

Liquid-liquid dispersion operations may be performed in agitated tanks provided by high shear rate impellers (e.g. turbines). As in the case of gas dispersion, the interfacial surface between phases is generated by the agitation and varies with it. Also the droplet size of the dispersed phase will depend on the degree of the agitation being the result of the two opposite processes of disruption (due to agitation) and coalescence. Liquid-liquid systems are characterised by major complexity with respect to solid-liquid and, also, gasliquid dispersions. In particular, in some cases, it is not possible a priori to establish which one of two immiscible phases will perform as dispersed and continuous one.

Mean diameter of drops

The main global parameter describing the characteristic of dispersion is the mean droplet diameter dp. Considering that the droplets are characterised by a dimension distribution, the average diameter usually adopted is the surface-based mean diameter (Sauter diameter) dS obtained starting from the ratio of total volume to total surface of all dispersed drops in the volume:

 di3

ntot

 a



Vdisp S disp



n i 1 ntot

i

6

nd i 1

i

2 i

ntot d S3 dS   6ntot d S2 6

Sauter mean diameter

ntot= total number of drops  = disp. phase hold-up a = specific surface, m2/m3

6 dS  a

Liquid-liquid dispersions Liquid-liquid dispersion operations may be performed in agitated tanks provided by high shear rate impellers (e.g. turbines). As the impeller action is produce high liquid deformations (shear) in order to deform drops of disperded phase and break them in smaller ones, this action depends on the ratio of fluid kinetic energy at the impeller tip speed to a surface-tension stress based on D which define the Weber Number (We): C  ND  C N 2 D 3  We    2

D

C= density of continuous phase = surface tension

Correlation for dS Several empiric correlation have been proposed to estimate mean drop diameter depending on agitation conditions, relevant to different mixing devices. Rushton turbine:

Static Kenics mixers: Where:

d S D  0.058 1  5.4  We 0.6

d S D  0.35We 0.6 f 0.4

C v 2 D We   D  pipe diameter, m v  average fluid velocity, m/s f 

DP  friction factor, 2 C v 2 L

Design of agitation (1) Decide the type and geometry of the tank and the agitator. (2) Find the performance of the installation first, including the size, rotating speed and power, then scaling up to commercial scale.

Scaling up criteria geometric similarity all the sizes have same ratio, such as H/D. dynamic similarity there are same velocity ratio and direction on corresponding points. kinetic similarity all have same forces ratio on corresponding points (with same Re, Fr or We). where： Re：the ratio of inertia to viscous forces Fr： the ratio of inertia to gravitational forces We = N3D2 / ：the ratio of inertia to surface tension 80

Relevant parameters D = impeller diameter (m), N = impeller speed (1/s) Ws = shaft power, Wbrake = brake power (W or HP) T = tank diameter, Z = liquid level m. Viscosity Pa.s, density kg/m3, Surface Tension N/m Qi = impeller pumping capacity (m3/s)

Scale-Up Based on geometrical similarity, if possible Power consumption predicted by curves of NP vs NRe ROT for power – – – –

½-1 hP per 1000 gal of thin liquid gives “mild” agitation 2-3 hP per 1000 gal gives “vigorous” agitation 4-10 hP per 1000 gal gives “intense” agitation Actual power delivered to the liquid

Ratio of Dimpeller to Dvessel

– Dispersing a gas in a liquid – 0.25 – Contacting two immiscible liquids – 0.4 – Blending – 0.6 or more

Smaller the impeller, higher the impeller speed

Scaling up criterion (1) power consumption per volume (Pw/V) =Const. Used for constant liquid properties and relatively small scaling-up ratio. Good for turbulent mixing dominated situation in fully turbulent flow. N13 D12  N 23 D22 (2) Tip speed constant Keep the agitator torque constant in a geometrical analogue system. Suitable for operation of high head.

N1 D1  N 2 D2 (3) Reynolds number, Re= Const.

N1 D12  N 2 D22

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Scaling up criterion (4) Froude number, Fr=Cost. N12 D1  N 22 D2

(5) Webber number, We= Const.

N12 D13  N 22 D23 Which scaling up process should be used? depends on the practical situation.

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