stirring theory and practice

Mixing tanks and their fittings Stirrer types and their operating characteristics Sealing of stirrer shafts 12 Shear stress on the particulate material beinig mixed Statistical theory o

Stirring: Theory and Practice Marko Zlokarnik

Prof: Dr Marko Zlokarnik

GrillparzerstraBe 58

8010 Graz

Austria

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Mixing tanks and their fittings

Stirrer types and their operating characteristics

Sealing of stirrer shafts 12

Shear stress on the particulate material beinig mixed

Statistical theory of turbulence 21

Experimental determination of state of flow flow and its mathematical

Vortex formation Definition of geometric parameters

Chemical reactions for determining micro-mixing

Dimensionless representation of material functions

Short introduction to dimensional analysis and scale-up

Primary and secondary quantities; dimensional constants

Drawing-up of a relevance list for a problem

Determination of the characteristic geometric parameter

Constructing and solving of the dimensional matrix

Determination of the process characteristics

Fundamentals of the model theory and scale-up

Remarks regarding the relevance list and experimental technique

Dealing with material systems with unknown physical properties Experimental methods for scale-up 73

Advantages of use of dimensional analysis

Range of applicability of dimensional analysis

3.3

Degree of mixing and molar excess

Material systems without density and viscosity differences

Material systems with density and viscosity differences

Optimization to minimum mixing work

Scale-up of the homogenization process

Homogenization through rising up gas bubbles

Physical fundamentals of mass transfer

Saturation concentration c, of the gas in the liquid

Definition of the characteristic concentration difference Ac

Consideration of the absorption process from a physical and industrial

Determination of k ~ a 132

Mass transfer characteristics for the G / L system

Mass transfer relationship: experimental data

Sorption characteristics in the coalescing system water/air

Sorption characteristics in coalescence-inhibited systems

Sorption characteristics in rheological material systems

Sorption characteristic in biological material systems

Interfacial area per unit volume a

4.6 Gas fraction (gas hold-up) in gassed liquids 153

4.6.1 Definition of E 154

4.6.2 Determination of E 154

4.6.3 Process relationships for c 155

4.10 Bubble coalescence 165

4.11 Foam breaking 175

4.11.1 Methods and devices for foam breaking 176

4.11.2 Foam centrifuge and foam turbine 177

4.11.3 Minimum rotor tip speed 179

4.11.4

4.12 Special gas-liquid contacting techniques 183

4.12.1 Hollow stirrers 183

4.12.1.1 Application areas 183

4.12.1.2 Suction, power and efficiency characteristics

4.12.1.3 Comparison of hollow stirrer and turbine stirrer

4.12.2.4 Plunging water jet aerators

4.12.2.5 Horizontal blade-wheel reactor 197

Suspension o f Solids in Liquids (S/L System)

Classification of the suspension condition

Distribution of solids upon suspension

Relevance lists and pi spaces

Specification according to the nature of the target quantity n,

Specification according to particle property d, and/or w,, 21 1 Suspension characteristics with d, as the characteristic particle

Power requirements upon suspension

Contents I ix 5.3.2.4

Power requirement for the critical stirrer speed n,

Scaling up in suspension according to the criterion n,

Suspension characteristic with w,, as the characteristic particle

Determination of the particle sinking velocity in the swarm w,,

The relevance list and the pi space

Final discussion from the viewpoint of the dimensional analysis

Establishing of scale-up criteria 230

Effect of geometric and device-related factors on the suspension

characteristic 233

Homogenization of the liquid in the S / L system

Mass transfer in the S / L system

Physical basis of mass transfer in the S / L system

Process characteristics of mass transfer in the S / L system

Effect of coalescence and of pv on d3z

Effect of viscosity 251

Droplet size distribution 253

Effect of stirrer type and material system

Effect of the mixing time

Scaling up of dispersion processes

Mass and heat transfer upon dispersion

Mathematical modeling of the dispersion process

7 Intensification o f heat transfer by stirring 272

7.1.1 Determination of cli 273

7.1.2 Dimensional-analytical description 273

Generalized representation of the heat transfer characteristic by

Taking non-Newtonian viscosity into consideration

Optimization of stirrers for a maximum removal of reaction heat Heat transfer for G/L material systems

Heat transfer in S/L systems

Indirect heat exchange for Ap > 0

Heat transfer in L/ L material systems

Heat transfer in G/L/S material systems

Mixing and stirring in pipes

Straight, smooth or rough pipe without fittings

Mass transfer in pipe flow

Mass transfer in pipe with static mixer

Heat transfer 3 11

Heat transfer in pipe with static mixer

Dispersion in pipe with static mixer

Micro-mixing and chemical reaction

Pipe reactor with a jet mixer

Pipe reactor with static mixer

Modeling of mixing processes in pipes

Contents I xi

8.6.2 Pipe with Tee mixer 323

8.6.3 Pipe with static mixer 323

Literature 328

Subject Index 360

Permeation of scientific method into this field largely took place in the second half of the twentieth century, during which all the other disciplines in process technology evolved from “arts into sciences” Particularly chemical and process engineers in the chemical industry and in research have studied this topic in- tensively, since chemical, biochemical and biological processes can only take place when all the reaction partners are brought into close contact

This book represents a brief summary of the state of the art in the field of stir- ring technology from the viewpoint of the author It particularly focuses on recent research results, account being taken of scientific literature published up to the

Only someone who has studied this topic intensively since the 1950’s can fully appreciate the immense advances made feasible by new physical measuring methods and computers Forty years ago determination of the stirrer speed still required a

stop-watch or a stroboscope!

Today, the whole field of classical stirring technology can be regarded as largely accessible to scientific method, so that a standard design for stirrers for any stirring operation on an industrial scale is ensured Research is shifting increasingly to mathematical simulation of stirring processes In the future, interesting sugges- tions for industrial practice can be expected from this work

I wish to express my sincere thanks to my friend Dr Dr.-Ing e.h Juri Pawlowski for his many helpful suggestions, to my long-standing colleague and co-worker, Dr.-Ing Helmut Judat from Bayer-Leverkusen for putting at my disposal the exten- sive, partly jointly collected, scientific literature from the 1950’s to the 1970’s, and

to Dr.-Ing H.-J Henzler from Bayer-Elberfeld and to Dr.-Ing habil Peter Zehner from BASF-Ludwigshafen for the critical reading of a chapter of the manuscript

Classification of Unifying Processes with Regard to the Material Systems Involved in the Unit Operations Mixing, Stirring and Kneading

tion of common salt from powdered or crystalline common salt and water require different equipment and different procedures from those used for the preparation

of bread dough, modelling paste with coarse or fine clay, or a concrete mixture

It is standard practice to classify mixing operations with regard to the state of aggregation of the major component in the mixture, since the same state of ag- gregation will generally be present in the final mixture From the standpoint of process technology it is relevant, whether a gas is sparged into a liquid or a liquid is sprayed into a gas

A further distinction must be made with regard to the degree of uniformity of the liquid phase: low viscosity liquids will be much easier to handle than highly viscous paste-ldce liquids In this respect the classification of fields of work given in Table 0.1 is recommended

Tab 0.1

aggregation of the major component

Classification of mixing operations according to the state of

State ofoggregotion Unit operotion Stondord mixing equipment

gaseous mixing, spraying mixing chamber, nozzle

solid (particulate) mixing, blending mixer

To avoid misunderstandings, it should be pointed out that the above-used mixing terms do not enable a clear distinction to be made between the unit operation as action and as aim Thus the term mixing includes both the unit operation of blend- ing or intermingling and the result of this unit operation namely the preparation

of a (stochastically or molecularly homogeneous) mixture Finally one can mix a

furnace preferably by supplying heat (This is also the case with the English terms mixing and blending.)

When a material system, in which liquid phases predominate, is stirred, this action can result in miscible liquid phases forming a molecularly homogeneous mixture (“solution”) In the case of immiscible liquids, on the other hand, a dis- persion (possibly an “emulsion”) will result If stirring is performed to increase heat or mass transfer, the purpose is to accelerate this operation and the inherent mixing of the liquid phases is of secondary importance

A similar situation exists in the case of the term kneading There are screw machines whose primarily task are the mixing or conveying of paste-like compo- sitions In such cases the kneading itself is of secondary importance, although it cannot be ignored

It should therefore be borne in mind that the available terms such as mixing,

tell us little or nothing about the result of the operation (In this they differ from other unit operations such as grinding, filtration, distillation, etc Here, the expected result is fully described by the term used.)

This book has been exclusively devoted to stirring for a number of reasons: in- tensive research in this field has been carried out in the last 10-15 years, largely

books devoted to the other unifying operations (mixing of solids, mixing in ex- truders) have been published’) in the German language literature, making consid- eration of these topics unnecessary

It is neither the task nor in the ambit of the author, to mention all the significant scientific contributions over the last 50 years within the field covered by this book, much less, to honour them properly This task has already been carried out at reg- ular intervals in various reviews over the years It is therefore appropriate, to refer

to these reviews” A researcher is very well advised to consult them before he begins his own research in a special field of stirring technology

1) Ralf Weinekotter - Hermann Gericke: Juri Pawlowski:

Mischen von Feststoffen (Mixing of

particulate solids)

Springer-Verlag 1995 Salle+Sauerlander 1990

Transportvorgange in Einwellen-Schnecken (Transfer proceses in single-screw extruders)

ISBN 3-540-58567-2 ISBN 3-79 3 5 -5 5 28-3

2) Mixing - Theory and Practice, Vol 1 + 2 + 3

(Ed.: V.W Uhl, Y.B Gray)

Academic Press, New York 1966, 1967, 1968

Nagata, S.: Mixing - Prinaples and

Application

Kodansha Ltd Tokyo & John Willey, New

York 1975

ISBN 0-470-62863-4

Kneule, F.: Riihren (Stirring)

3 Adage, Decherna Frankfurt/Main, 1986

Verfahrenstechnische Berechnungsrnethoden

T e i l 4 Stofiereinigen in fluiden Phasen (Unifying processes in fluid phases) Authors: F Liepe, W Meusel, H.-0 M&kel,

B Platzer, H WeiBgerber VCH Verlagsges., Weinheim 1988

ISBN 3-527-26 205-9

ISBN 3-921567-48-3

drag coefficient of a sphere in a fluid flow

pipe flow friction factor

heat capacity at constant pressure

stirrer diameter

bubble diameter, usually represented by d32

mean gas bubble or liquid droplet diameter (“Sauter diameter”; eq (6.8)) particle or droplet diameter

terminal (final) bubble diameter

inside tank or pipe diameter

diffusion coeficient

effective dispersion coefficient (in axial direction)

difference

enhancement factor in chemisorption; eq (4.76)

energy spectrum of vortices

activation energy in chemical reactions

force

mass flow (rate of mass transfer, oxygen uptake)

stirrer distance from bottom of the vessel (bottom clearance)

heat transfer coefficient, definition eq (7.1)

total liquid depth (liquid height) in vessel

momentum

mass flux; eq (4.7)

heat flux, eq (7.1)

rate constant in eq (1.1)

wave number of vortices

gas side mass transfer coefficient

liquid side mass transfer coefficient

volume-related over-all mass transport coefficient, eq (4.9) base dimension of length

pipe length

mixing length in pipe flow

flow index in pseudoplastic fluids

mass, rn = pV

enhancement factor in physical absorption; eq (4.88)

base dimension of mass

stirrer speed

number of stages

normal stress ( x = 1 or 2); eq (1.50, 1.51)

pressure, pressure difference (pressure drop)

power, stirrer power

volume throughput

liquid throughput, brought about by a stirrer

heat flow (rate of heat transfer)

velocity components in the x-, y-, z-direction

mean flow velocity

mean values of velocity fluctuations ( u ; = @) over-all heat transfer coefficient, eq (7.2)

velocity; superficial velocity

superficial flow velocity (uG K qG/Dz)

liquid volume (ungassed)

sinking velocity of single particles; eq (5.17)

sinking velocity of a particle swarm; eq (5.20)-(5.22) chemical conversion X = (co - ct)/co

deformation

shear rate, eq (1.41)

temperature coefficient of the viscosity, eq (7.6)

thickness (of film, layer, wall)

mixing power per unit mass e = P / p V

gas hold-up (gas fraction in liquid)

mixing time

kinetic energy per unit mass, E k i n / m = (1/2)ma2/m = v 2 / 2

Kolmogorods micro-scale of turbulence; 2 = (v3/&)'I4; eq (1.6)

relaxation time, eq (1.53)

heat capacity per unit volume at constant pressure

interfacial, surface tension

standard deviation under given conditions (,)

variance

variance coefficient

mean residence time r = V / q

shear stress, eq (1.41)

related to stirrer speed

start condition, initial value

particle (solid or liquid)

related to throughput

terminal (final) value

value at the time t

technological scale, full-scale

drag coefficient of a sphere in fluid flow

friction factor in pipe flow

Hat1 Hatta number, 1.order reaction

E u = Ap/(pv2)

Fo = at/d2

Fr = n2d/g Fr' = F r p / A p

- Intensification of heat transfer between a liquid and a heat transfer surface;

- Suspension (and possible dissolution) of a solid in a liquid or slurry formation;

- Dispersion (or sparging) of a gas in a liquid (gas-liquid contacting)

Dispersion (or emulsification) of two immiscible liquids;

The term homogenization is used, if a uniform liquid phase has to be realized, e.g a molecularly homogeneous mixture of several miscible liquids or equalization

of concentration and temperature differences during a chemical reaction in the liquid phase (The same term is used in the food industry for a completely different

operation, namely for L/ L (liquid/liquid) dispersion under extreme shear condi-

Intensification of heat transfer in a stirred tank can represent, especially in case

of viscous liquids, an important stimng operation, particularly if a strongly exo-

operation consists of reducing the thickness of the liquid boundary layer on the tank wall and realizing liquid transport to and from the heat exchanger surface

If particulate matter has to be dissolved in a liquid or if a chemical reaction cata- lyzed by a solid is involved, the particles must be suspended from the vessel bottom,

so that the total surface can participate in the process In continuous processes a stochastically homogeneous distribution of the solid in the bulk of the liquid is required, so that the solid particles can be transported with the liquid from stage to stage (for example in a cascade crystallization process) In this intensive suspen- sion process, the solid is, as a rule, subjected to high mechanical stress, which can result in its attrition

In the case of dispersion in a L / L or L / G (liquid/gas) systems, one fluid phase is distributed in the other in the form of fine droplets or gas bubbles to accelerate

mass transport between the two phases In suspension polymerization the stirring conditions are adjusted so that a particular desired droplet size distribution results Often different stirring operations must be carried out simultaneosly, an example being solids-catalyzed hydrogenation, in which the stirrer disperses the gas (hydro- gen) in the liquid phase, swirls up the catalyst particles (e.g Raney nickel) from the bottom of the reactor and intensifies the removal of reaction heat In such cases the stirring conditions are determined by that stirring operation which is the bottle- neck in the process

1.2

Mixing Equipment

1.2.1

Mixing Tanks and Auxiliary Equipment

The mixing tank or stirred vessel is the most commonly used piece of stirring equipment (It is also the most commonly used chemical reactor) This is due to its considerable flexibility as regards the flow conditions, which can be realized in

it Mixing tubs and storage tanks are the second most commonly used pieces of mixing apparatus

The tank diameter is restricted to D 5 4.6 m on transport grounds A further increase in liquid volume is therefore only possible by an enlargement of the vessel height Two disadvantages have thereby to be taken into account: a) the stirrer shaft becomes longer and support bearings may be required along its length; b) mixing times increase (see Fig 3.6) (For most stirring operations the most favorable aspect ratio HID (liquid height to vessel diameter) is HID z 1)

Section VIII Internal fittings include: baffles, coils, probes (e.g thermometer, level

indicators) and feed and drain pipes All of these fittings can influence the stirring process

If an axially positioned stirrer is operated in a vessel without inserts, the liquid is set in rotation and a vortex is produced In the case of rapidly rotating stirrers and

low viscosity liquids, the vortex can reach the stirrer head with the result that the stirrer entrains the gas in the liquid (see section 1.4.5.2) This is generally unde- sirable because it results in an extraordinarily high mechanical stress on the stirrer shaft, bearings and seal, due to the absence of the “liquid bearing” This ofien leads to the destruction of the stirrer Even when the vortex formation causes no gas entrainment, rotation of the liquid is always undesirable if a two-phase system with different densities is concerned, since the centrifugal force counteracts the stirring process

The rotation of liquid in cylindrical tanks is prevented by the installation of baffles So-called “complete baffling” is realized with four baffles (flow interrupting

strips) D/10 in width, where D is the inner diameter of the vessel, arranged along the entire vessel wall Dead zones in the flow direction behind the baffles can be

Baffles are not necessary, if stirring is carried out in a container with rectangular cross-section (e.g basins or pits) or when the stirrer is mounted laterally in the tank wall In the case of weak stirring, rotation of the liquid can be prevented even

in cylindrical tanks by installing the stirrer eccentrically and/or at an angle to the tank axis In this case, however, uneven mechanical stress in the stirrer shaft must

be accepted

A jacketed vessel wall is sufficient to supply or remove relatively small quantities

of heat The usual configurations are shown in Fig 1.2

To transfer larger quantities of heat, the installation of coils is necessary A helical coil (Fig 1.3a) is only efficient with axially working stirrers, since they produce good liquid circulation in the annular space between the helical coil and the wall

On the other hand, the liquid circulation produced by radially working stirrers is strongly deflected by a helical coil, so that the flow through the annulus between the coil and wall is suppressed For such stirrer types, it is advantageous to arrange the coil in vertical loops along the vessel wall (meander coil, Fig 2b) This arrange- ment does not deflect the radial flow pattern, but prevents bulk rotation of the liquid

to such an extent that baffles are often superfluous

1 5

1.2 Mixing Equipment

6 I 1 Stirring, General

The heat-exchange tubes can also be arranged into bundles and installed instead

of baffles (Fig 1 3 ~ ) These heat exchangers possess a particularly large surface area and are therefore mainly used in biotechnology, e.g in penicillin and enzyme production, because the operating temperature in such processes has to be kept below 40°C, resulting in extremely small temperature differences

1.2.2

Stirrer Types and Their Operating Characteristics

The stirring operations discussed in the introduction can obviously not be per- formed with a single type of stirrer There are many types of stirrers appropriate for particular stirring operations and particular material systems In this section only those stirrer types will be discussed which are widely used in the chemical industry and for which reliable design guidelines exist The dimensions of stirrer types have also been standardized to a large extent [ 1611

In Fig 1.4 the stirrer types are arranged according to the predominant flow pat- tern they produce, as well as to the range of viscosities over which they can be effectively used 90% of all stirring operations can be carried out with these stan- dard stirrer types The flow patterns obtained with typical radially and axially con- veying stirrers are shown in Fig 1.5

Of the stirrer types which set the liquid in a radlal motion - or into a tangential flow in the case of high viscosities - only the turbine stirrer*) (so-called “Rushton turbine”, a disk 2d/3 in diameter supporting 6 blades each d / 5 high and d/4 wide

[474]) belongs to the high speed stirrers It can be sensibly utilized only with low viscosity liquids and in baffled tanks Its diameter ratio Dld is 3-5 The turbine stirrer causes high levels of shear and hence is well suited for dispersion processes

[438] and thus has rounded stirring arms It is installed with small bottom clear- ance at a Dld ratio of 1.5 and can be used both with and without baffles Due to the small bottom clearance it can be used with strongly fluctuating filling levels (e.g during emptying), since it can efficiently mix even small liquid volumes

PFAUDLER [438] has developed the so-called “Cryo-Lock-System”, enabling enamel- coated-BE vessels according to DIN 28136 to be equipped with impellers of d > 600

mm via a manhole of I 600 m m in diameter It is a stirrer with four paddles of different design (straight, pitched paddles, TurbofoilJ-o) its paddles being arranged

on the hub in an X-configuration rather than in a cross configuration The fasten- ing of the impeller hub to the impeller shaft is realized inside the tank by first con-

finally heating to produce the connection [316]

Cross-beam, grid and blade stirrers are slow-speed stirrers and are used at

D / d = 1.5 to 2 both with and (in the case of viscous liquids) without baffles They

are particularly suitable for homogenization

* In the German literature on mixing the

Rushton turbine is referred to as

Scheibenriihrer: “disk stirrer” This is a

misleading choice of words, since it is not the disk which effects the stirring, but the blades

it supports [ G37]

Fig 1.4 Classification of stirrers according to the predominant

flow pattern they produce and to the range of viscosities over

which they can be effectively used

Fig 1.5

baffled tank, generated by

A - axial-flow propeller and a

B - radial-flow turbine stirrer

8 7 Stirring, General

The slow-speed anchor stirrer is generally utilized with close wall clearance ( D / d I 1.05) to intensify heat transfer in high viscosity liquids

Pitched-blade turbines, and in particular propeller stirrers, belong to the group

of high-speed stirrers, which accelerate the liquid in the axial direction Both stirrer types are generally utilized with low viscosity liquids and baffled tanks They are suitable for homogenization and suspension of solids Multiple-stage pitched-blade stirrers are required to enhance the axial flow in vessels of H / D > 1 (e.g in fer- menters), especially in viscous media Examples of such stirrers are cross-beam

heim, Germany [0.14] They are operated at low speeds at D / d = 1.5 with baffles and at D l d = 1.1 without baffles and are used for homogenization, suspension of solids, and dispersion

The very slow-speed helical ribbon stirrer is a close-clearance stirrer ( D / d x 1.05)

and is so operated that the liquid on the wall is transported downwards Under these

conditions this stirrer is the most suitable of all the stirrer types for homogenizing high viscosity liquids

In addition to these frequently used stirrer types, there are special designs of which only a few will be mentioned here

In stirrer types acting according to the rotor/stator principle, the rotor is a turbine

stirrer (Fig lh), or a toothed ring (as implemented in the “Ultra-Turrax” from IKA

Janke & Kunkel [227], Fig 1.7), which is surrounded by a baffle ring as stator In this way extremely high shear forces are realized in a small space (“wet grinding”)

If the stirrer consists of a flat toothed disk, as e.g the ZAR design [52G] (Fig 1.8), the liquid is accelerated radially in a small ring away from the disk and then rapidly decelerated This produces high shear forces even in the absence of a stator ring and baffles These two stirrer types are particularly suitable for emulsification and dispersion in a wide range of viscosities (e.g in the production of pigment paints)

In hollow stirrers the stirrer head is hollow and is connected via a hollow shaft to the gas space above the liquid The suction generated behind the stirrer edges by rotation according to the Bernoulli principle can thus be used to supply gas to the liquid Hollow stirrers are suitable for enhancing mass transfer in gas/liquid con-

I

Fig 1.6 A stirrer based on the rotor/stator

1 9

1.2 Mixing Equipment

Fig 1.7 Ultra-Turrax" of IKA Janke & Kunkel [227]

Fig 1.8 Toothed or dissolver disk; ZAR design [526]

tacting, combining the roles of a stirrer and a gas-supplying device Fig 1.9 shows the so-called "pipe stirrer", a simple and very effective hollow stirrer All hollow

stirrers operate at high speed and at D f d x 3-5 in baffled tanks

Manufacturers of mixing equipment offer special stirrer designs for particular problems, also to gain a market edge Examples are: Interprop@, Isojet@ (Fig l l O ) ,

Paravisc, Coaxial systems (frame stirrer + Viscoprop%) from EKATO [0.14]; Alpham, Sigma" (Fig 1.11) and Zeta@ stirrers and coaxial stirrers (in different combina-

Fig Hollow stirrer, type pipe stirrer [252]

10 I I Stirring, General

Fig 1.10

Isojet'" and Interprop" of EKATO [0.14]

PR - propeller, EIPR - EKATO Interprop"

tions) from Stelzer RLihrtechnik [ 5261; Turbofoilc (Fig 1.12) from Pfaudler-Werke

(Fig 1.13)

The advantages and material savings currently achievable with systematic stirrer

Fig 1.11 Ruhrtechnik [526]

SigmaH stirrer of Stelzer

I l 1

1.2 Mixing Equipment

development are shown by the EKATO Interprop" stirrer (EIPR) It offers a space saving, twin-wing construction with an at least 30% saving in material and at the same time is clearly superior to the propeller stirrer in the solids suspension and to turbine stirrer in mass transfer in G / L (gas/liquid) systems [134]

In the course of the advent of biological waste water treatment, civil engineers have developed very different types of surface aerators (see [ 6281 and surface aera- tion, Section 4.12.2)

1.2.3

Nozzles and Spargers

Nozzles enable the kinetic energy of a liquid propulsion jet to be utilized for dif- ferent purposes In the first instance one can distinguish between one- and two- component nozzles Single fluid nozzles are generally used as atomizer nozzles, in which the kinetic energy of the liquid propulsion jet is utilized for dispersion of its own There are, however, also pneumatic atomizer nozzles, which belong to two- component nozzles [ 5711

In a few cases the energy-rich propulsion jet of a sinfle fluid nozzle is also uti- lized for homogenization of liquid mixtures in storage tanks (see Homogenization

in Storage Tanks, Section 3.7)

If the kinetic energy of the propulsion jet (gas, steam, liquid) is utilized accord- ing to the Bernoulli principle for generating suction, the nozzles are referred to as ejectors or ejector nozzles These are not dealt with here

If, on the other hand, the energy of the liquid propulsion jet is utilized in a mix- ing chamber, which is connected to the diffuser, for sparging the gas throughput into fine gas bubbles, the nozzles are referred to as injectors These are utilized

Fig 1.13 Maxflo T-Hydrofoil-Impeller"

(PMD) of Prochem [183, 3561

12 1 Stirring, General

to an increasing extent in gas-liquid contacting in biological waste water treatment (see Spargers, Section 4.12.3) They are also suitable as spargers in bubble columns and for pneumatic mixing in storage and equalizing tanks (see Homogenization in storage tanks, Section 3.7)

Spargers are utilized for distributing gas throughput in bubble columns and to a large extent in aerobical waste water treatment plants (so-called activated sludge ponds) Formerly they consisted of a perforated, slotted or punched steel sheet, but they are currently generally made of porous plastic There are two types: tubular aerators (“filter cartridge”) and plate aerators (“dome”) (see [629] and Aeration with Spargers, Section 4.12.3)

I

1.2.4

Sealing of Stirrer Shafts

In closed stirred tanks the rotating shaft must be sealed against the tank lid (or against the tank bottom) The type of seal depends upon whether the gas or liquid space has to be sealed, on the stirrer speed and on the pressure difference Ap be-

tween the operating pressure (system pressure) in the tank and the outside pres- sure (generally atmospheric pressure)

In choosing the type of seal and the seal material, it has also to be taken into account that most “free-flying’’ shafts are subject to flexional stress, which causes

radial shaft displacement in the seal face According to [0.14] this can amount to 0.1

between the lower bearing and the seal face It has further be taken into account that the sealing material at the shaft entry from the tank lid can come into contact not only with the gas space above the liquid but also through splash and foam for- mation with the whole contents of the tank This is found to be particularly prob- lematic in the presence of a third solid phase (e.g solid catalysts)

A survey of seal types is shown in Fig 1.14

Immersion seals are only practicable at low stirrer speeds and negligible Ap

values between inside and outside Silicone oils of different viscosities can be used

as the sealing liquid A seal cage or lantern ring can withstand relatively large Ap

under the influence of water Plaited asbestos impregnated with oil or with graphite powder was formerly generally used as compression packing in the chemical in- dustry Currently cotton cord impregnated with lubricating plastics (Teflon”, PTFE)

is used

At high shaft speeds and negligible Ap values labyrinth seals can be utilized,

whose narrow openings build up a high dynamic pressure [log] Lip seals are

practicable at Ap values < 1 bar, particularly for laboratory devices They are made

of rubber or silicone plastics and often have to be cooled Generally slip properties have to be maintained with a liquid (usually silicone oil)

For high pressure differences the usual type of sealing device is the mechanical seal, of which there are a range of designs (internal and external single and double mechanical seals; with and without throttle bushing, with or without pressure relief) Some of them can be dismantled and replaced in filled tanks under pres-

1 c 3 < 25 < 300

Labytinth seal

Lip seal Mechanical seal

Magnetic clutch

Fig 1.14 Classification of shaft sealing devices with regard to

system pressure and the shaft speed

sure (Ap = 16 bar [62]) with the stirrer at standstill This requires an additional seal

for shaft at standstill Seal faces can be produced from carbon, metals (steel, stain- less steel, Ti, Ta) or industrial ceramics and carbides (Sic, WC) For satisfactory sealing, lubrication of the seal face and cooling is generally unavoidable Upon in- troducing the stirrer shaft from underneath, the so-called sub-level seals have to be

permanently flushed to protect the seal faces from solids

Typical operating limits for single sliding ring seals are velocities of u I 5 m/s

and Ap < 7 bar and for double sliding ring seals Ap < 26 bar (in special designs up

to 40 bar) [0.14, 5261

For high pressure and high-speed shafts hermetic sealing of the space on the

product side via a split-pot in contact-free torque transmission by way of a mag-

netic coupling remains the only safe alternative Example: EKATO “Safety magnetic

14 I I Stirring, General

can be transmitted at operating pressures < 100 bar and temperatures < 300°C depending upon the design ( E M S 2040 to 2100) [583]

Detailed information over sealing possibilities can be obtained from the manu- facturer’s brochures [0.14, 62, 5261

1.3

Mechanical Stress

In dealing with the problem of mechanical stress one has to distinguish between the aspects which concern device construction and those which are of concern to the device users Information over the mechanical forces, which operate on the stirrer, the shaft, the shaft bearings and the shaft seal, together with the critical stirrer speed etc., can be obtained from the brochures of the stirrer manufacturers

[0.14, 5261 and from research papers such as [123, 393, 4201 In this section only those aspects which are of interest to the comparatively large group of users of mixing equipment will be considered

1.3.1

Stress on Baffles

Flow deflecting fittings are unsteadily influenced by the turbulence produced by the stirrer and by the boundary layer separation Resonance can thereby occur, knowledge of which is indispensable in the design of large stirred tanks Kipke [271] investigated experimentally the dependence of the dynamic stressing of baf- fles upon stirrer type, the number of baffles and their arrangement in the vessel

He came to the following conclusions:

Fmax/Faverase values were obtained: 1.3 for cross-beam stirrer; 1.G for MIG 07; 1.8 for turbine stirrer, and 2.5 for propeller stirrer These values were independent of the tip speed of the stirrer

- The pressure loading on the baffles decreased independently of the stirrer type approximately directly proportionally with increasing number z of baffles:

Ap a 2-l In the case of propeller stirrers, the relationship Ap a z-’I2 was found

- The pitch of the baffles was only investigated with the MIG 07 stirrer It was found that any pitch in a positive or negative direction from the radial position resulted in an increase in pressure loading

1.3.2

Stress on Stirrer Heads

The fluctuating hydraulic forces, which operate on stirrer heads [273], are expressed

1.3.3

Tank Vibrations

Tank vibrations are observed upon stirring in homogeneous material systems at low viscosities Viscous liquids strongly damp these vibrations On the other hand particularly strong vibrations occur in vessels when gassing low viscosity liquids,

such as those currently in use in biotechnology In [393] it was found that pro-

peller and MIG stirrers, operating in G/L dispersions in a relatively narrow range

of Reynolds numbers, produced strong vessel vibrations, whereas turbine stirrers in the industrially interesting stirrer speed range produced a relatively even vibration spectrum with low overall vibrations

1.3.4

Wear of Stirrer Heads

Kipke [274] investigated the wear of stirrer heads, a problem that occurs mainly in ore dressing (mineral and clay slurries) The wear of (primarily) axially working

pitched-blade turbine, propeller and INTERMIG stirrers were studied The stirrers

were made out of brittle acrylic glass (PMMA) and the material systems used were aqueous slurries of corundum (dp = 0.5 and 1.0 mm; qm = 2.5-10 wt.-%) The wear of the stirrers (measured by weight loss) during the operating time t was con- verted to decrease in diameter, which gave a wear rate defined as u ( t ) = a d ( t ) / a t

The theoretical prediction of the relationship u cc u3 ( u being the tip speed of the stirrer, comparable with the collision rate of the particles) was fully confirmed It was independent of stirrer type The same applied for the dependence u = f ( t ) It was found that the wear is greatest at the beginning with the not yet reduced stirrer diameter at which the tip speed was highest Later on it leveled off until a constant value was reached, which is virtually independent of the starting conditions The relationship u = f(t) was suitable for estimating the operating lifetime of stirrers It is only necessary to supply the maximum permissible diameter reduc- tion d/do In practice d/& values in the range of 0.9 to 0.99 are acceptable

The wear rate increased directly proportionally up to q m = wt.-5%, above which it decreased The cause is the ever greater collision frequency between the particles themselves The influence of the particle diameter d , on the wear rate is consider- able: u K d i This relationship can also be proven theoretically [274]

As regards the influence of the type of solid on the wear, there are only ap- proximate data The wear is roughly 50 times smaller with lime particles than with

corundum, with the corresponding values for glass and quartz being 3 and 1.1

16 I 7 Stirring, General

respectively Kipke [274] recommended, in the case of stirrers vulnerable to wear, that pilot plant experiments be carried out with the original material system and the stirrers be made out of acrylic glass and that the results be converted with his formulas

1.3.5

Shear Stress on the Particulate Material Being Mixed

The hydrodynamic stress on the particles in reactors is in many industrial pro- cesses of crucial importance It can be welcome, e.g in dispersion processes in

G / L (gas/liquid) and L/L (liquid/liquid) systems It can, however, also be undesir- able, e.g in many agglomeration and crystallization processes, particularly in bio- technological systems Thus, for example, mammal cells can be destroyed even at low shear forces The morphological structure of the cell clusters, important for product formation in fungal cultures (penicillin and citric acid), can be negatively influenced by shear forces, as can the biofilm formation of microorganisms and enzymes on solid carriers (immobilisation of bio material), etc It is therefore not

recent biotechnogical literature (e.g 183, 349, 379, 423, 501, 562))

It is not possible to quantify the mechanical shear in bioreactors Besides this, experiments with biologically active systems are very costly Model systems on the basis of blue clay flocks are therefore investigated Their destruction is monitored with laser scanning microscopy [ 2131

The “blue clay HFF of Witterschlick” (98 wt.-%, particle diameters < 2 pm) is

Germany) to flocks Their size and stability can be adjusted over a wide range (2 to

2000 pm) by varying the flocculant concentration A further advantage is that the size of the flocks is retained when the shear stress is reduced, the reagglomeration

of the flocks being very slow, can hence be ignored

cells attached to carriers) it was established that a qualitative correspondence exists between the shearing off rate for mamal cells and the flock destruction rate [213]

At constant mechanical stress the flock destruction kinetics is described by a 1

order rate equation:

where dF, dFo, dFco are the flock diameters at time t, at time t = 0 and after the de- struction is completely finished, respectively; t = co was independent of the ex- perimental conditions It is the time necessary to attain the original particle size again which can take a very long time Therefore the stable terminal flock size was taken to be that at a destruction rate d(dF)/dt = 5.5 x pm/s [28] It is known

as the comparison flock diameter dFc

7.3 Mechanical Stress

Tests in vessels of different size ( D = 0.29-0.975 m) have proved that the flock

destruction depended strongly on the power per unit volume P/V, but was virtually

independent of the stirrer tip speed Fig 1.15 proves this conclusively: in geo-

metrically similar mixing vessels of different sizes a given P/V value was always

attained at another tip speed

The left part of Fig 1.15 shows the results for a propeller stirrer, the right part those for an anchor stirrer The difference between the two stirrer types proved, that, for a large-surface stirrer the power was evenly distributed over the vessel

This finding demonstrates that the mixing power does not relate to the whole

vessel volume, but only to the volume V, = wd’h ( h - stirrer height) swept by the

stirrer, assuming that most of the power has been dissipated therein [28, 2141

This is proved by the results in Fig 1.16, which were obtained with 6 stirrer types

and different values of d/D and h/d In the left part of the figure, the comparison flock diameter dFc is plotted as a function of P/ V and in the right part as a function

of P/Vs The relationship is well correlated with P/Vs for the stirrer with d/D =

0.33 and corresponds approximately to

The propeller stirrer with d/D = 0.55 and the INTER-MIG with d/D = 0.65 lay

on the fitting line, when V, was set equal to V

Comparable results in bubble columns of different sizes, whose spargers were sintered plates or perforated plates, gave similar results (see Fig 1.17) The fitting line corresponds to the relationship:

where P,/pV represents the adiabatic compression power per unit mass [197]

the same shear stress is present, if in small and in large vessels the geometric simi- larity and

are ensured This is consistent with the Kolmogorov’s theory of locally homoge-

neous and isotropic turbulence [289], see section 1.4

In turbulent flow range, turbulence exists on the micro- and the macro-scale The micro-scale 3, is responsible for the shear stress, which for a particle size ( dp) which

is significantly smaller than 1 (i/dp = 5-25), can influence the particle size of the dispersed phase

The micro-scale 1 of turbulence is according to Kolmogorov described by 3, =

( V ~ / E ) ~ / ~ [289] The shear condition on a small-scale is similar to that on a large- scale when the physical properties, here the kinematic viscosity v, and the geometry

20 7 Stirring, General

I

Fig 1.17

P,/pV for bubble columns with different spargers and different

liquid heights; from (197)

Comparative flock diameter d, as a function of

are kept constant

L ( E / V ~ ) ’ / ~ = idem

This statement confirms eq (1.4)

the macroscopic flow had to be considered It was found that the stretching flow component had a significantly greater effect on breakup than the shear flow com- ponent Measurements of the power consumption of various stirrer types in visco- elastic fluids verified that the axially working stirrers exerted a considerably higher portion of stretching flow component as compared to the radially working ones The effect of shear history on size, density and structure of flocs during floccu-

terns was long inaccessible to theoretical treatment It is therefore not surprising that it was first tackled by the statistical theory of turbulence [20, 57, 209, 2891

Later numerical methods were applied, which are based on the laws of conser- vation of mass and momentum, and are restricted to stationary, isothermal and

I 21

7.4 Flow and Turbulence

rotationally symmetrical flow of homogeneous incompressible Newtonian liquids The stirrer is thereby approximated for the calculation of turbulent flow by a tan- gential jet 1288,4411, and for laminar flow by a cylinder [46-48, 50, 981 The stirred

tank is split up into a number of zones, to which one can assign characteristic flow patterns and analytically describable velocity profiles Models with up to 8 zones have been developed, but only two models (for stream ejected by the stirrer and for circulation flow) have been able to explain the experimental results satisfactorily [ 4401

Currently a wide range of calculation methods and powerful computers are avail-

able In the EU, 13 research groups have joined forces to tackle the numerical and

experimental investigation of flow conditions in stirred tanks [ 1221 Both commer- cially obtainable CFD codes and those further developed in the universities are available (CFD - Computational Fluid Dynamics) Simple K - E and advanced turbu- lence models are utilized and compared with one another ( K - kinetic energy per mass; E - stirrer power per mass) The flow produced by the stirrer is described by approximate calculations of the 3-dimensional (3D), non-steady state circulation of the stirrer paddles

For experimental determination the flow pattern produced by the stirrer was initially visualized using different photographic methods (e.g [ 574, 497]), but hy- draulic probes were also used to determine the pressure distribution (e.g [ 1351)

and velocity distribution (e.g [437]) Also, convection probes (spherical probes) and

pressure probes (Prandtl‘s Pitot tube) were used Later constant temperature hot- wire/hot-film anemometry was used Currently contactless laser doppler velocim- etry (LDV)/anemometry (LDA) is exclusively utilized

1.4.2

Statistical Theory of Turbulence

In his treatise “The local structure of turbulence in an incompressible viscous

of free turbulence as random variables, which are in general terms accessible to probability theory This assumes local isotropic turbulence Thus the probability distribution law is independent of time, since a temporally steady-state condition is present For these conditions Kolmogorov postulated two similarity hypotheses:

1 The laws of statistical distribution for locally-isotropic turbulence are clearly determined by the kinematic viscosity v and the power per unit mass E = P / p V

Dimensional analysis gives the following relationship for the linear dimension I

of a turbulence element:

1 = ( V 3 / & ) ] ’ 4

where 1 is the dimension of the smallest turbulence element, whose energy due to the viscosity is directly converted into heat i has become known as the Kolmogorov’s micro-scale of turbulence

22 I 1 Stirring, Genera/

2 Energy transfer from larger to smaller turbulence elements is independent of viscosity for all turbulence elements in between with dimensions > i

According to Kolmogorov the turbulent flow field (Re > lo4) can be understood

as a superposition of turbulent eddies of different orders of magnitude This view

is based on the interpretation of the temporal course of turbulent fluctuating velocities at a point in the flow field, which can be explaned as the superposition

of different frequencies of different amplitudes (amount of fluctuating velocities) These eddy elements can be characterized accordingly by particular frequencies or after a Fourier transformation by particulat wave numbers k The largest eddies are produced by the stirrer head They give their kinetic energy up cascade-like to ever smaller eddies This energy transport is not prevented by the viscosity forces, as long as the eddies and their Reynolds numbers Re, are sufficiently large The vis- cosity forces only dominate in the case of small eddies and ensure that the energy

of flow is converted into (dissipated as) heat In this range of eddy sizes local iso- tropy prevails, although the main flow is anisotropic In other words, the small eddy elements characterized by high wave numbers are completely statistically independent of the main flow

On the other hand, the so-called macro-scale of turbulence A is given by the size

of the primary eddies and is of the order of magnitude of the stirrer diameter Thus the precondition for the existence of locally isotropic turbulence is sufficient difference between both scales and in a high Re number [ 3641

The division of the kinetic energy into the individual eddy regions takes the form

of an energy spectrum E ( k ) Only those parts of the spectrum in the region of small eddies are of interest, in which locally-isotropic turbulence is expected Two regions can be clearly distinguished, for which different relationships apply (see Section 1.4.2.2)

In a well regarded contribution, Kipke [277] ventured the speculation that the turbulence field could not be adequately described in the laboratory by the Reynolds

or Froude numbers, a “healthy compromise” had therefore to exist between the turbulence theory and the theory of similarity In this regard he referred to the drag characteristics of the sphere and the controversy between Prandtl and Eiffel at the beginning of the twentieth century Prandtl had however been able to show that the laminar boundary layer around the sphere was converted into a turbulent bound- ary layer by a purely geometrical interference (“trip-wire”), which already at lower Reynolds numbers rips off the boundary layer and thus reduces the drag

In other words, this apparatus-related boundary condition is not included in any dimensionless number, the drag characteristic of the sphere is unequivocally de- scribed in the space { cd, Re}, where c d is the drag coefficient Such a situation

is echoed in stirring technology, where the flow conditions in a mixing tank also essentially depend upon whether baffles are present or not, and this fact is only

This problem is due to the fact that stirring experiments are generally carried out

in small laboratory devices ( D < 1 m), in which the micro-scale turbulence is pre-

that mixing operation in which macro-scale turbulence is essential The latter is