Mixers

Mixing is one of the important unit operation widely used from reaction to

finishing stages in chemical industry. A production (chemical) engineer has to

operate the running and modifications with the installed type for the particular

process or recommend one in case of plant erection or process design. The

selection or modification with these equipments is highly subject to the set of

properties of material being handled. Mixers are meant to shift the non-

homogeneity of a batch to a homogenous state. The degree of success in this

operation is never the hundred percent, since we can’t assume that a molecule A

will take the very next position to the molecule B and so on. Our auditing analysis

is therefore subject to spot sampling methods that take concentrations at

randomly selected locations in a sample in to consideration to estimate the

overall mixing efficiency of the entire batch.

Different mixers being employed follow three1 mixing phenomenon: the small-

scale random motion (diffusion), the large-scale random motion (convection) and

the interchange of particles by virtue of slip zones (shear). Mixers are employed

both for solids and liquids phases with varied interests. These include be but not

limited to blending of ingredients, cooling or heating purposes, drying or roasting

of solids, reaction engineering, coatings, agglomeration or even size reduction.

Confining our focus the mixing of solids, powders and particles, our selection is

subject to a set of properties2 which include: particle size distribution, bulk

density, true density, particle shape, surface characteristics, flow characteristics,

friability, state of agglomeration, moisture or liquid content of solids, density,

viscosity and surface tension, and temperature of ingredients. Referring our case

to the nature of solid particles, we have two classifications to cater for: non-

1 Perry’s Chemical Engineering Handbook, Solid-Solid Operations and Equipment, Section 19, pg. 12 2 Perry’s Chemical Engineering Handbook, Solid-Solid Operations and Equipment, Section 19, pg. 10

cohesive solids and cohesive solids. Further is the discussion over the types of

mixers for this classification.

For Non-Cohesive Solids

Mixers for non-sticky solids have a wide variety available for consideration. This may

range from free-flowing powders’ preferences to heavy pastes’ options. Mixing could be

carried3 out by agitation, tumbling, centrifugal action and impact forces. Following is a

brief about the options for discussed type of solids:

Internal Screw Mixer

It consists of a vertical vessel with a screw rotating to achieve the circulation of material

and secondly the elevation of material. This results in intermixing of solid grains as well

as shear action to the ones in contact with the screw or the walls of container. The feed

enters from bottom usually with aim to nullify the gravity factor which could escape the

molecules without desired mixing. Two vessel shapes are normally used for this

category, the cylindrical and the conical. On the basis of screw movement, it could

further be classified4.

3 McCabe Smith, Unit Operations of Chemical Engineering, Mechanical Separations, Vol 7, pg 979 4 Perry’s Chemical Engineering Handbook, Solid-Solid Operations and Equipment, Section 19, pg. 15

Type I: Conical shaped vessel, with a screw orbiting the centre of axis of the vertical

tank and also rotating around its own axis

Type II: Conical shaped vessel, with a screw fixed at the centre and rotating around its

own axis

Type III: Cylindrical vessel with a screw in centre and rotating around its own axis

Internal screw mixers are normally used for free-flowing grains and other light solids. In

type II, the conical tank is such tapered that with increase in height the area swept

increases.

Ribbon Mixer

Suitable for light and finely divided materials to fibrous sticky feed, ribbon mixer is

operated in both batch and continuous orders. It consists of a horizontal vessel with two

blades or ribbon in opposite directions with rotating at different speeds to intermix the

feed batch. The operation size5 could be as large as 34m3 for heavy ribbon mixers. The

size of ribbon widely affects the operational advantages. For example, broad ribbon can

be used for lifting or conveying purposes, while a narrow ribbon can cut the materials.

The type is further classified on construction parameters with differing features6 of

ribbon cross section and pitch, clearances between outer ribbon and shell, and number

of spirals etc.

5 McCabe Smith, Unit Operations of Chemical Engineering, Mechanical Separations, Vol 7, pg 979 6 Perry’s Chemical Engineering Handbook, Solid-Solid Operations and Equipment, Section 19, pg. 12

Tumbling Mixers

Tumbling mixers include mixers in which the vessel rotates, mixing the feed to optimum

levels, similar to tumbling mill that aim for size reduction. The closed vessel rotating

about its axis can handle heavy solids and dense slurries through diffusion mixing. The

shapes could include5 and are not limited to V-mixer, double cone, rotating cube. The

equipment main include internal sprays for addition of liquids to facilitate the mixing

process. Baffles could also be installed in an attempt to reduce segregation.

The retention time in a tumbling mixer is fixed since initial blending is rapid followed by

gradual uniform mixing. Excess time may affect and even decrease the quality of mixing

levels.

For Cohesive Solids

Cohesive solids employ maximum consideration in terms of mixer selection and

operating parameters due to influence of rheology and forces of cohesion. The power

consumption for this type of mixers is high due to these factors. Mixing of sticky solids

however is supported7 by shearing, folding, stretching and compressing elements.

7 McCabe Smith, Unit Operations of Chemical Engineering, Mechanical Separations, Vol 7, pg 980

Muller Mixers

Suitable for heavy solids and pastes, muller mixer applies smearing, rubbing and

somewhat skidding action to achieve the desired mixing levels. Its working action is

similar to that of mortar and pestle. It has several types, three most common include:

Stationary-pan mixer, Rotating-pan mixer and Countercurrent-pan-muller mixer. The

roller wheels move in a circular chamber to ride over the material, producing shearing

action that causes size reduction as well as intermixing of material.

Change-can Mixer

Used for blending of viscous liquids & light pastes like food and paints, its most used

types are pony and beater mixer. In pony mixer, the can rotates to produce centrifugal

action to mix the materials, while in beater mixer, the agitator rotates to do the job. The

vertical shaft contains blades and paddles which are slightly twisted. When the mixing is

complete, agitator head is raised, lifting the blades out of can and the material can be

drained by tilting it.

Kneader Mixers

It is used to mix deformable or plastic solids by squashing the mass flat, folding it over

and squashing it once more7. It may tear the mass and shear it between the blades and

walls of mixer. The power requirements for this type of mixers are relatively high, esp. in

case of stiff materials. Examples (in order of power requirements) include: two-arm

kneader, disperser, masticator (intensive mixers), banbury mixer (internal mixers), and

continuous kneaders.

The two-arm kneader with minimum power requirements handles suspensions, pastes

and light plastic materials. A disperser with heavier construction body and more power

consumption is suitable for additives and coloring agents into stiff materials. Masticator

with maximum work capacity can work on scraping rubber and plastic materials. The

body is heavier than disperser and consumes more power.

In internal mixers, the chamber is sealed during the working time; making dispersions of

feed in liquid usually water. Example of such a type is Banbury mixer, a heavy-duty two

arm mixer in which the agitators are in form of interrupted spirals. The turning frequency

is 30 to 40 rpm. Kneaders work both in batch and continuous operation with equipment

parameters differing accordingly.

Paddle Mixers

These mixers are open air chambers with agitators scooping the materials and dropping

them again to those chambers, thus achieving the mixing levels via relocation of

material. The lifting action of blade is adjusted to the desired pace. This cross missing

configuration provides a homogenously mixed product. The use is effective even in

cases where bulk densities of component materials vary greatly. The design and bends

of the paddles are precisely made to ensure shear mixing in addition to convective one.

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PREPREPREPRELIMINARYLIMINARYLIMINARYLIMINARY

Deciding on and choosing the size of a type of a mixer consists in finding the optimum parameters for the implementation of the desired procedure. Frequently, optimization is limited by constraints such as costs, bulk or physical limits. This approach consists in choosing a certain number of parameters: • Type of agitators and position

- Radial discharge rotors - Axial discharge rotors - Mix discharge rotors - Angled discharge rotors - Dispersion/emulsification rotors

• Geometry of the tank (size, shape) • Rotation of the rotor (speed, rate of discharge) • Length of mixing • Imposed physical conditions (pressure, temperature)

The people who make these choices rely on their knowledge and experience to make them and choices become additionally complex because of a certain number of factors of which the most frequent follow: • The nature and rheology of products can lead to complicated expressions of a certain number of parameters and specifically of their

respective progress during the mixing process. More precisely in the case of non Newtonian liquids (when viscosity of liquids is directly related to the speed of shearing) for which is observed non linear progress of the required power and the rate of flow of circulation in respect to the rotation speed of the agitator. This is observed in rheoliquidifying liquids (fruit juice, blood), threshold or Bingham liquids (paint, varnish, mayonnaise, toothpaste), rheothickening liquids (wet grit, starch suspension, pizza dough) or thixotropic liquids (yogurt).

• Constraints regarding some parameters because of experience or technologic and economic reasons, such as the peripheral speed return from one type of mixer to another, shearing rate, speed of flow or pumping limit the margin of action for the calculation of the other mixing parameters. It is a limiting factor but we must consider that these constraints, in the end, lead to a more rapid result by minimizing choices.

In practice, choosing an agitator becomes a compromiseIn practice, choosing an agitator becomes a compromiseIn practice, choosing an agitator becomes a compromiseIn practice, choosing an agitator becomes a compromise: ::: aaaa dominant parameter isdominant parameter isdominant parameter isdominant parameter is establishedestablishedestablishedestablished and calcul and calcul and calcul and calculated and ated and ated and ated and thenthenthenthen the other parameters the other parameters the other parameters the other parameters are checked to insure they are checked to insure they are checked to insure they are checked to insure they are sufficientare sufficientare sufficientare sufficient....

VMI recommends and implements the following method: StepStepStepStep 1 1 11 ............................................................... Identification of the type of mixing to perform

�

StepStepStepStep 2 2 22.................................................................................................................................................................................................... Inventory of the characteristics of mixing materials

�

StepStepStepStep 3 3 33 ............................................. Identification of the global characteristics of mixing rotors

�

StepStepStepStep 4 4 44 .....................................................................Choice of the rotors

�

StepStepStepStep 5 5 55 ................................................... Calculation of the various mixing parameters (tank – rotors)

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STEPSTEPSTEPSTEP 1:1:1:1: Identification Identification Identification Identification of the type of mixing to performof the type of mixing to performof the type of mixing to performof the type of mixing to perform

• SSSSolid / liquidolid / liquidolid / liquidolid / liquid mixturesmixturesmixturesmixtures- Soluble powders Soluble powders Soluble powders Soluble powders

� Dissolution � Homogenizing

- Non soluble Non soluble Non soluble Non soluble powderpowderpowderpowderssss� Placing in and/or maintaining in suspension � Homogenizing � Dispersion

• LiquidLiquidLiquidLiquid / l / l / l/ liquidiquidiquidiquid mixtures mixtures mixtures mixtures- Miscible liquidMiscible liquidMiscible liquidMiscible liquids sss

� Placing in and/or maintaining in suspension � Homogenizing � Dilution

- Immiscible liquidsImmiscible liquidsImmiscible liquidsImmiscible liquids � Emulsion

• Complex rheComplex rheComplex rheComplex rheololololoooogy of viscous mixturesgy of viscous mixturesgy of viscous mixturesgy of viscous mixtures� Placing in and/or maintaining in suspension � Dissolution � Homogenizing � Dispersion � Heat transfer � Grinding

STEPSTEPSTEPSTEP 2: 2: 2: 2: Inventory of the characteristics of mixing materialsInventory of the characteristics of mixing materialsInventory of the characteristics of mixing materialsInventory of the characteristics of mixing materials

• LiquidLiquidLiquidLiquidssss- Density - Viscosity - Percentage - Initial and final temperature - Type of discharge

• SolidSolidSolidSolidssss

- Nature - Percentage - Density - Granulometric dimensions and distribution - Settling speed - Wettability - Solubility

• GaGaGaGassss

- Nature - Flow - Pressure - Solubility

STEPSTEPSTEPSTEP 3:3:3:3: Identifi Identifi Identifi Identification of the gcation of the gcation of the gcation of the globalloballoballobal c c ccharacteristicharacteristicharacteristicharacteristics sss of mixingof mixingof mixingof mixing rotorrotorrotorrotorssss

• Flow mainly generated (axial or radial) • Importance of the pumping effect (high, medium, low) • Importance of the shearing effect (high, medium, low) • Capacity of generating turbulence (high, medium, low)

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STEPSTEPSTEPSTEP 4:4:4:4: ChoiceChoiceChoiceChoice of of of of rotorrotorrotorrotorssss

You must then chose between the varieties of rotors offered by VMI the one that is the best adapted to the mixture you want to produce. Your choice should be based on the following: • Intrinsic characteristics of the rotors taking into account the preferred type of flow, knowing that frequently a compromise must be made

between the type of discharge (axial, radial, turbulent…) and mechanical effect generated (circulation, shearing, …), • Laboratory tests, • Financial criteria: example = choice in order to achieve the best Nq/Np performance to minimize installed capacity, • Functional criteria: example = choice of a rotor that is the easiest to clean.

Currently VMI offers the following agitation rotors:

1. Profiled triblade 7. Centripetal 13. Break=up

2. Two way profiled triblade 8. Deflocculator 14. Butterfly

3. PSVB four blade 9. Sevin with inlets 15. Saw teeth

4. PSVH four blade 10. Centrifugal 16. Anchor blade

5. PA four blade 11. Centri=deflocculator 17. Rotor=stator

6. Water propeller 12. Cutting

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Table I

Main FlowMain FlowMain FlowMain Flow RotorRotorRotorRotor Type Type Type Type MainMainMainMain FuFuFuFunctionnctionnctionnction Power Power Power Power NNNNPPPP

Pumping Pumping Pumping Pumping NNNNQQQQ

Shearing Shearing Shearing Shearing StrengthStrengthStrengthStrength

Water propeller (6) Circulation 0.21 to 0.28 0.58 to 0.68 Very low

Profiled triblade (1) Homogenizing liquid/liquid 0.34 to 0.60 0.84 to 0.87 Very low

Two way profiled triblade (2)

Dissolution, incorporation charges

0.76 to 1.22 1.15 to 1.2 Very low

PSVB four blade (3) Dilution/Dissolution 1 to 1.95 1 to 1.73 Very low

PA four blade (5) Dilution/Dissolution 1.8 to 2.2 1 to 1.73 Very low

AXIALAXIALAXIALAXIAL

SEVIN with inlets (9) Dissolution/Dispersion 0.4 to 0.55 0.75 to 0.85 Medium Centripetal (7) Dilution/Dissolution 1.6 to 2 1.1 to 1.3 Low Centrifugal (10) Dissolution 2.5 to 4.5 3 to 3.8 Medium Saw teeth (15) Dispersion 0.23 to 0.42 0.19 to 0.31 High

Deflocculator (8) Dispersion 0.34 to 0.8 0.37 to 0.44 High Centri=deflocculator (11) Dispersion 1.1 to 2 0.67 to 0.79 High Rotor/Stator wide slots

(17a) Dispersion/Emulsion 2.1 to 5.9 0.82 to 0.9 Very high

RADIALRADIALRADIALRADIAL

Rotor/Stator narrow slots (17b)

Dispersion/Emulsion 2.3 to 6.2 0.55 to 0.6 Very high

Note: NP, NQ and shearing strength are expressed for equivalent diameters

• Power: 53dN

PN p ρ= (P: agitation power; ρ: density; N: rotation speed; d: rotor diameter) is the coefficient

of drag from the agitator when in the liquid and represents power usage. • Pumping:

3dNQN P

Q = (QP: pumping flow rate; N: rotation speed; d: rotor diameter) is the dimensionless

expression of the pumping flow rate for the agitator. • Shearing strength indicates the capacity of the rotor in breaking the friction effect exerted by two infinitesimal

layers of liquid sliding against one another. Shearing is usually stated as speed of shearingeV=γ& , expressed as

s=1, a value that is very difficult to measure. PERFORMANCE MOBILES

MARINE

TRIPALE BI-DIRECTTIONNELLE

QUADRIPALE

SEVIN

DEFLOCULEUSE

CENTRIFUGE

TRIPALEPROFILEE

ROTOR/STATOR FL

ROTORSTATOR FE

CENTRIPETE

0

0,5

1

1,5

2

2,5

3

3,5

Pouvoir de cisaillement

Rendementd

edébitN

q/Np

MAINTIEN EN SUSPENSION

HOMOGENEISATION

DILUTIONDISSOLUTION

DISSOLUTIONDISPERSION DISPERSION

EMULSION

Très Faible Faible Moyen Fort Très Fort

ROTOR PERFORMANCE

Shearing Strength Very Low Low Medium High Very High

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Table II Solid / Liquid Mixtures Liquid / Liquid Mixtures

Soluble Powders

Non Soluble Powders Miscible Liquids Immiscible Liquids

Complex Rheology for

Viscous Mixtures

Heat Transfer

Suspension Homogenizing 1 3 6 7

(*) 1 3 6 7(*)

High

circulation capacity Dissolution

Homogenizing

1 2 3

.

7 10

11 .

1 2.

Dilution 1 3 7 10

.

Dispersion 8 9 10 11 12 .13 15 17

(**)

High shearing strength

Emulsion 8 16 .

2 8 9 14

15 17 .

1 3 6

16 .

(*) Triblade � efficient for high volumes at low rotation speeds Four blade � efficient for low and medium volume at medium rotation speeds Water propeller � efficient for high volumes requiring strong circulation Centripetal � very efficient for dissolution because of the right compromise between circulation and shearing (**) Deflocculator / Sevin � a Sevin insures better circulation at equivalent power input, specifically for high volumes Centrifuge

� very efficient for complex dissolutions Break=up � very efficient for placing compact materials in suspension Centri=deflocculator � very good compromise between the centrifuge and deflocculator

STEPSTEPSTEPSTEP 5555: ::: CalculCalculCalculCalculation of the various mixing parametersation of the various mixing parametersation of the various mixing parametersation of the various mixing parameters

1.1.1.1. Diameter, number and speed of one or more mixing rotorDiameter, number and speed of one or more mixing rotorDiameter, number and speed of one or more mixing rotorDiameter, number and speed of one or more mixing rotor(s)(s)(s)(s)

These calculations are performed taking into account as main parameters one or several criteria for a precise mixture: • Criteria for mixing efficiency

= peripheral speed, = recirculation rate therefore capacity of the turbine, = length of the mixing process.

• Criteria linked to the rheology of the product (the higher the viscosity of the product, the higher the diameter of the rotor at low speed)

• Economic criteria

GuideGuideGuideGuide for selectingfor selectingfor selectingfor selecting the the the the D D DDtool tool tool tool ////DDDDtanktanktanktank ratioratioratioratio in the tank Table III

DDDDtooltooltooltool / D/ D/ D/ Dtanktanktanktank TypeTypeTypeType of of ofof RotorRotorRotorRotor SpeedSpeedSpeedSpeed ((((rpmrpmrpmrpm)))) Low viscosity productLow viscosity productLow viscosity productLow viscosity product Viscous productViscous productViscous productViscous product****

3000 0,1 0,2 Rotor/Stator 1500 0,15 0,25

1500 to 750 0,2 0,3 500 to 250 0,25 0,5 170 to 90 0,3 0,6 Propeller or Turbine

60 to 30 0,5 0,8 Anchor or butterfly blade 10 to 200 0,9 à 1

*according to the number of movements

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Guide for selecting the peripheral sGuide for selecting the peripheral sGuide for selecting the peripheral sGuide for selecting the peripheral speed and the recirculation ratepeed and the recirculation ratepeed and the recirculation ratepeed and the recirculation rate Table IV

TYPE TYPE TYPE TYPE OF MIXTUREOF MIXTUREOF MIXTUREOF MIXTURE

Speed inSpeed inSpeed inSpeed in m/s m/s m/s m/s Recirculation Recirculation Recirculation Recirculation volume bac/hvolume bac/hvolume bac/hvolume bac/h

Maintaining in suspension, circulation: slow sedimentation product 0,5 to 1,5 50 to 200 Maintaining in suspension, circulation: fast sedimentation product 1,5 to 2,5 200 to 300 Liquid/liquid homogenizing 2,5 to 4 300 to 400 Liquid/solid homogenizing Relatively equal apparent densities Low concentration dissolution: 10 to 20 % max

4 to 5

400 to 700

Solid /liquid homogenizing Very different apparent densities High concentration dissolution: up to 50 %

5 to 8

700 to 1000

Dispersion facile 8 to 10 800 to 1200

Difficult dispersion • Products that swell • Extremely fine products • Mashing

15 to 20

1000 to 1500

Guide for selecting the number ofGuide for selecting the number ofGuide for selecting the number ofGuide for selecting the number of rorororotortortortors in thes in thes in thes in the tanktanktanktank Table V

ViscosityViscosityViscosityViscosity Pa.s Pa.s Pa.s Pa.s No.No.No.No. of of of of

momomomovementsvementsvementsvements Height of workHeight of workHeight of workHeight of work (Nb of (Nb of (Nb of (Nb of

timestimestimestimes ØØØØ))))Flow rate factorFlow rate factorFlow rate factorFlow rate factor K K KK0000

0.001 (eau) 8 to 3 1.3 <0.1 3 to 2 1.2

0.1 to 10 1 movement

2 to 1.5 1 10 to 30 1.5 to 1 0.8 30 to 60

1 or 2 movements 1 0.6

60 to 100 0.8 0.5 100 to 1000 0.65 0.35

> 1000 2 movements minimum

0.5 0.2

2.2.2.2. CalculCalculCalculCalculation of the ation of the ation of the ation of the characteristiccharacteristiccharacteristiccharacteristic parameters of the mixer parameters of the mixer parameters of the mixer parameters of the mixer.

• Sizes used: - D: diameter of the mixing tool (m) - N: rotation speed of the tool (t/s) - ρ: apparent density of the liquid (kg/m3)- µ: viscosity of the liquid (Pa.s) - NP0: Number for nominal capacity - NP: Number for corrected capacity - NQ: Number of pumping actions - KS: Metzner=Otto constant to calculate shearing - K: Consistency index (Pa.sn=1 ) = n: exponent of rheoliquidifying; K and n are determined by a measure of

viscosity where µ = Kγn=1

• Calculation of Reynolds number (Re) Newtonian liquids: Re =ρ x N x D2/µNon Newtonian liquids: Reequivalent = (ρ x N2=n x D2)/K

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• Calculation of the nominal capacity number NP0 = f(Re) Experimental values ofExperimental values ofExperimental values ofExperimental values of N N NNP0P0P0P0 = f(Re) = f(Re) = f(Re) = f(Re) (N(N(N(NP0P0P0P0 = 1 for = 1 for = 1 for = 1 for Re = 10 Re = 10 Re = 10 Re = 104444))))

Table VI Four bladeFour bladeFour bladeFour blade

ReReReRe TribladeTribladeTribladeTriblade ProfiléeProfiléeProfiléeProfilée

Water Water Water Water PropellerPropellerPropellerPropeller PAPAPAPA PSVBPSVBPSVBPSVB PSVHPSVHPSVHPSVH CentripetalCentripetalCentripetalCentripetal DeflocculatorDeflocculatorDeflocculatorDeflocculator

SEVIN SEVIN SEVIN SEVIN with with with with inletsinletsinletsinlets

1 / 100 22,4 36,2 31,5 53 94 128 2 59 60 13,5 21 19 31 55 77 3 29,5 44 8,8 14,3 12,4 22 39 57 4 23,5 36 7,6 12,4 11,4 18 34 49 5 19,1 30 6,5 10,5 9,5 16 30 41 6 16,2 26 6,2 10 9 12 24 31 7 14,7 23,2 5,3 8,6 7,6 11 22 28 10 11,2 18 4,1 5,7 5,2 9,5 16 23 20 6,8 10 2,8 3,8 3,2 6 10 14 30 5,3 7,6 2,4 3,1 2,7 4,7 7,9 10,5 40 4,4 6 1,9 2,8 2,2 4 7 9 50 3,8 5,2 1,8 2,6 2 3,4 6 7,7 70 3,2 4,4 1,5 2 1,8 2,8 5 6,2 100 2,7 3,6 1,2 1,7 1,3 2,3 4 5,2 150 2,2 2,8 1,2 1,4 1,2 2 3 3,8 200 1,8 2,6 1,1 1,1 1,05 1,8 2,5 3,1 250 1,6 2,2 1,06 0,95 0,95 1,7 2,4 2,8 300 1,5 1,8 1, 0,95 0,95 1,7 2,2 2,6 500 1,2 1,4 0,95 0,86 0,86 1,5 1,8 2,1 1000 1,1 1,2 0,95 0,86 0,86 1,2 1,4 1,6 5000 0,94 1 1 0,95 0,95 1,05 1 1,05 10000 1 1 1 1 1 1 1 1 50000 1,03 0,88 1,06 1 1 0,96 1 0,97 100000 1,12 0,84 1,1 1,05 1,05 0,95 1 0,9

• Calculation of Froude number (Fr) if required (appearance of a vortex) Fr = N2 x D/g (g=9,81 ms=2)

A vortex will be considered formed if Fr ≥ 3

• Calculation of corrected capacity number NP

- If Fr ≤ 1 (no vortex), then NP = NP0 - if Fr ≥ 3 (vortex), then NP = NP0 x Fry et y = (a – Log Re) / b

radial effect rotors: a = 1 b = 40 axial effect rotors: a = 2,1 b = 18

• Calculation of absorbed pump power Pab (in W) Pabs = NP x ρ x N3 x D5

• Calculation of turbine flow rate Q (in m3/s) Q = NQ x N x D3

• Calculation of drag flow rate Qe (the viscosity of the liquid is taken into account) Qe = Q x K0 (flow rate factor, see Table V)

• Calculation of recirculation rate TRC (in volume / hour) Directly deducted from the drag flow rate Qe and the volume V of the tank

• Calculation of mixing time Tm

Tm = K x V/Qe where K is an experimental coefficient varying from 10 to 10000 (tests from Grenville and Co in 1992 or Nienow in 1997) If K is unknown the value for K0 can be used (Table V), and you will get: Tm = K0/TRC

• Calculation of peripheral speeds (VP), flow speeds (or transversal) (VF), and rising speed (VR)Peripheral Speed (in m/s) (linear speed of the extremity of the turbine)

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VP = π.D.N Flow Speed (in m/s) (linear speed of the liquid in the turbine)

VF = (4 x NQ x D x N)/πRising Speed (in m/s) (linear rising speed of liquids on the side of the tank)

VR = (4 x Q)/ π(Dc2 = D2) = (VF x D2)/(Dc

2= D2) with Dc = diameter of the tank