Agitation Handbook

Filipp Kars-Jordan Petri Hiltunen

Master of Science Thesis Stockholm, Sweden 2007

Agitation Handbook

Filipp Kars-Jordan Petri Hiltunen

Master of Science Thesis MMK 2007:23 MPK584 KTH Industrial Engineering and Management Machine Design SE-100 44 STOCKHOLM

Examensarbete MMK 2007:23 MPK584

Omrörningshandboken

Filipp Kars-Jordan Petri Hiltunen Godkänt Examinator Handledare 2007-02-28 Priidu Pukk Priidu Pukk Uppdragsgivare Kontaktperson Scanpump Tamás Kovács

Sammanfattning Examensarbetets syfte var att göra ett underlag för en handbok i industriell omrörning. Detta arbete belyser problematiken i samband med uppbyggnad av omrörare och tillhandahåller förslag och vägledning i hur man ska lösa många problem i samband med detta. Relevanta matematiska modeller och formler presenteras och vägledning ges i hur man skall tillämpa dessa i verkligheten. Uppbyggnaden av omrörningssystem är väldigt komplext och kräver stor know-how både vad gäller processen och matematiken som bör användas. Det finns vidare en mängd olika patenterade propellrar, turbiner och andra i omrörare ingående komponenter. Valet av rätt komponenter är också essentiellt för processen och vissa av dessa presenteras.

Man kan inte enbart med hjälp av denna bok bygga upp en välfungerande process, utan behöver hjälp av experter såvida man inte besitter djupa kunskaper inom turbulens och har stor know-how vad gäller komponenter som finns på marknaden. Denna handbok kan ses som ett hjälpmedel för att öka förståelsen för problematiken vid uppbyggnad av omrörningssystem och ger insyn i vad man kan kräva av företag som åtar sig uppgiften att bygga omrörare.

Master of Science Thesis MMK 2007:23 MPK584

AgitationHandbook

Filipp Kars-Jordan Petri Hiltunen Approved Examiner Supervisor 2007-02-28 Priidu Pukk Priidu Pukk Commissioner Contact person Scanpump Tamás Kovács

Abstract The goal of these master theses was to write an outcast for a handbook of industrial mixing. This book presents the problems and offers guidance and possible solutions in the process of building agitators. Relevant mathematical models and formulas are presented and it is explained under which circumstances these should be brought into play. Building an agitated process is a very complex task and requires good know how in both the process and the mathematics behind. There are numerous patented impellers and other components used in agitators and choosing the right components is of great importance for the efficiency of the process. Some of these components are thoroughly described in this work.

This book by itself is not sufficient to create a well working agitated process unless the user has a profound knowledge of turbulence and a good awareness about what components there are on the market and which should be acquired. Building an agitated process requires experts. This book can be used to gain insight in the difficulties of constructing agitators, also to gain an understanding of what can be expected and demanded from companies hired to assemble such processes.

Agitation handbook index

1. Turbulence...... 12 2. What is mixing?...... 16

2.1 GOALS OF MIXING ...... 17 2.2 SUSPENSION ...... 17 2.2.1 Sedimentation ...... 17 2.2.3 Degree of suspension...... 18 2.2.4 Particle motion in liquid...... 19 2.3 SOLID DISPERSION ...... 21 2.5 DIFFUSION...... 22 2.6 EMULSIFICATION...... 22 2.7 FERMENTATION...... 23 3. Rheology...... 24 4. Dimensionless numbers...... 28

4.1 REYNOLDS NUMBER ...... 28 4.2 POWER NUMBER (NEWTON NUMBER)...... 32 4.3 SCABA PUMPING NUMBER ...... 33 4.4 SCABA NUMBER & FLOW NUMBER ...... 34 4.4 DEGREE OF AGITATION...... 36 4.7 FROUDE NUMBER ...... 36 5. Liquid motion ...... 38

5.1 MIXING TIME ...... 38 5.2 CAVERNS...... 40 6. Scaba modular system...... 42

6.1 MOTOR...... 42 6.2 GEAR UNIT ...... 43 6.3 BEARING HOUSING ...... 44 6.4 SEAL HOUSING ...... 44 6. 5 SHAFT SEALS ...... 45 6.5.1 Stuffing box (S) ...... 45 6.5.2 Lip seal ...... 46 6.5.3 Mechanical seals ...... 47 6.5.4 Labyrinth seal...... 48 6.6 SHAFTS...... 49 6.7 COUPLINGS...... 49 6.7.1 Flange couplings ...... 49 6.7.2 Threaded coupling...... 50 6.8 BOTTOM STEADY BEARING...... 50 7. Tanks ...... 52

7.1 TANK GEOMETRY ...... 52 7.2 BAFFLES...... 54 8. Impellers...... 58

8.1 TURBINES...... 58 8.1.1 Rushton turbine ...... 58 8.1.2 6SRGT ...... 59 8.1.3 HD Turbine...... 61 8.2 PROPELLERS...... 61 8.2.1 SHP1&SHP18 ...... 61

8.2.2 Constant pitch...... 62 8.2.3 Gliding ratio ...... 63 8.2.4 SHPD...... 64 9. Stirrer installation...... 66

9.1 MOUNTING...... 66 9.1.1 Impeller position from wall or bottom...... 67 9.1.2 Number of impellers ...... 67 9.2 SELF-FREQUENCY...... 68 9.2.1 Over/under critical ...... 68 10. Wastewater treatment...... 72

10.1 FLOCCULATION ...... 72 10.2 DENITRIFICATION...... 73 10.3 DIGESTION ...... 74 11. Paper pulp industry...... 76

11.1 LIQUID MOTION IN PAPER PULP...... 76 11.2 DIMENSIONING PAPER PULP PROCESSES ...... 78 11.2.1 Different types of pulp ...... 78 11.2.2 Temperature ...... 80 11.3 PAPER PULP PROCESSES...... 80 12. Appendix...... 82

APPENDIX A...... 82 APPENDIX B...... 84 APPENDIX C...... 86 Notation...... 88

1. Turbulence

Turbulence is one of the most studied and unsolved phenomena of our century. The mathematical complexity of turbulent flow makes it impossible to use analytical methods and the approach must be statistical rather than deterministic. Since there is no strict definition of turbulence it is often described by the characteristics listed below:

• Irregularity – all turbulent flows are irregular and random. Thus, statistical methods are necessary. • Diffusivity – causes rapid mixing, increased momentum rates, heat and mass transfer. • Large Reynolds number – turbulence occur at large Reynolds numbers. • Three dimensional vorticity fluctuations – turbulence is three dimensional and rotational and can not exist in two dimensional flows. • Dissipation – kinetic energy of turbulence is consumed by viscous shear stress deformation work. Thus, to sustain turbulence, a continuous supply of energy is needed, otherwise the turbulence perish. • Continuum – turbulence can only occur in three dimensional space of size far larger then the molecular length scale of the matter in which the turbulence is to take place. • Turbulence is a property of a flow – turbulence is a property of a flow, not of the fluid itself.

First systematic studies on turbulence were done by Osborne Reynolds in the end of 1800th century. Reynolds studied flows in pipes and postulated what we call the Reynolds number (see chapter 3.3). Reynolds was also the first to introduce a statistical approach to Navier- Stokes equations (equations describe behaviour of flows and got their name from Claude- Louise Navier and George Gabriel Stokes) by rewriting the instant velocity into a sum of a mean and a fluctuating part. Navier-Stokes equations consist of one equation for conservation of energy, one for conservation of mass and depending on the nature of the problem one to three equations on preservation of momentum. Formulas presented here are for incompressible fluids, partly because these fluids are common in the industry, but mainly to simplify the formulas.

Navier-Stokes equations for incompressible fluids for conservation of mass and momentum:

ud i′ ud i′ 1 pd ′ ρ ud i′ + u′j −= + v (Eq 1.1) dt dx j ρ dxi dxi dx j

du i = 0 (Eq 1.2) dxi

ud ′ The variables u′ and p′ are instantaneous velocity and pressure and ν i in (eq. 1.1) can dx j be expressed as the viscous stress tensor ij = υ ′ = 2μsut ij where μ is molecular viscosity and

sij is the strain-rate tensor

1 ⎛ ud ′ ud ′ ⎞ S = ⎜ i + j ⎟ (Eq 1.3) ij ⎜ ⎟ 2 ⎝ dx j dxi ⎠

These equations are however impossible to solve because of their non-linear nature. The instantaneous velocity at a certain point is not static, but changes over the time and can vary a lot in different points in the flow, so the solution is far to complex to achieve even with the help of the most powerful modern computers. Reynolds introduced an approach to make up for the complexity of the turbulence phenomenon by breaking u′ into two terms and by that eliminating the instantaneous variable:

′ += uUu iii (Eq 1.4)

Ui is the mean part and ui is the fluctuating part. This approach gives the Reynolds stress tensor:

ij ρτ ∗−= uu ji (Eq 1.5)

Reynolds time-averaging however creates new unknowns but no new equations. Now there are ten unknowns (and still only four equations.

The equations for the kinetic energy can be obtained by multiplying the momentum equation

(eq 1.2) withU i , ui and the time averaging:

d ⎛ 1 ⎞ d ⎛ p ⎞ U j ⎜ UU ji ⎟ ⎜ j 2μ −+−= ⎟ ijjiijiiij −+ 2ν SSSuuUuuUSU ijij (Eq 1.6) dx j ⎝ 2 ⎠ dx j ⎝ ρ ⎠

d ⎛ 1 ⎞ d ⎛ 1 1 ⎞ U j ⎜ uu ji ⎟ ⎜ j 2ν iji −+−= ⎟ ijjijii −− 2ν SSSuuuuuSupu ijij (Eq 1.7) dx j ⎝ 2 ⎠ dx j ⎝ ρ 2 ⎠

The terms in the parenthesis on the right side of the equations (eq 1.6) and (eq 1.7) are pressure-, molecular diffusion and turbulent transport. The last two terms are related to turbulence production and viscous dissipation. The dissipation term in (eq 1.7) is the dissipation per unit mass and is referred to asε . The most common way to express ε is:

du du =νε i i (Eq 1.8) dxk dxk

k is kinetic energy per unit mass of the turbulent fluctuations (Prandtl 1945)

1 = uuk (Eq 1.9) 2 ii

Due to the non linear nature of turbulence models have to be used to describe the behaviour of flows in agitated vessels. The algebraic turbulence models use Boussinesq eddy viscosity approximation to compute the Reynolds stress tensor as the product of an eddy viscosity and the mean strain rate tensor. Due to the fact that several of the parameters in these algebraic models depend on the particular flow the algebraic models are, by definition, incomplete models of turbulence. Therefore engineers use other models when working with turbulence. The last two decades the majority of those working with turbulence have been using the so called two-equation models. These models are based upon the theories that for high Reynolds numbers all statistical quantities are functions only of the energy dissipation rate, ε and the kinematic viscosity, ν . Kolmogorov was first to introduce these functions for eddy viscosity, turbulence length scale and dissipation. Several other scientists have after Kolmogorov introduced their own approximations of energy dependence of the factors mentioned above. Unfortunately, many of those who work with flows in the industry choose wrong models for calculating on agitated flows. One of the most used models, the so called kε -model, should in fact not be used in the industry because of the conditions the flow is required to meet in order for this model to be used. Applications for which the kε -model fails and should not be used are as follow:

• Flow over curved surfaces • Separated flows • Flows in non-circular ducts • Flows with sudden change in mean rate of strain

In other words this model fails in virtually all industrial applications of agitated flows and the results should be treated with caution.

2. What is mixing?

Mixing as a concept is about reducing inhomogeneity. It can be inhomogeneity in concentration, phase or temperature. This might seem like a simple problem to solve, but is really a complex process involving theories of fluid mechanics and a large amount of know- how. In the industry mixing is needed in paper pulp manufacturing, sewage disposal, oil manufacturing, manufacturing of chemicals and in many other processes.

The media mixed can vary a lot and so can the goal of the mixing process. In chemical industries the mixing is often about getting a homogeneous fluid in shortest time possible while in some of the process steps of sewage disposal the mixing is applied in order to avoid stagnation and the stirring has to be as economical as possible i.e. lowest possible power ensuring the proper mixing. There are numerous terms describing the nature of the mixing process, shown in (table 2.1).

Table 2.1. The table below describes possible combinations of media to be mixed and the goals of the mixing process in terms accepted and used in the industry.

Most of these terms are more thoroughly described later and it will be shown how important Scanpump´s know how is to achieve the goals of the different processes, considering the choice of vessel, impellers and other tools (e.g. motors, gear boxes, etc.) used in the process.

2.1 Goals of mixing The goals of the mixing process can vary, so can the substances to be mixed. Different goals and substances require different equipment and approach. In the industry there are certain terms for certain mixing processes. Some of these terms are described in this chapter. 2.2 Suspension

Suspension is when solid particles are kept from settling in a tank to maximise the solids surface contact with the liquid. The solids may have different tasks at different processes for example it may act as a catalyst, go through a chemical reaction, or by dissolving into the liquid. Often the solid phase is introduced to the process trough the surface of the tank and there are solid particles that float and particles that sink depending on the density of the liquid and solid phase. Even if the solid phase has a higher density than the liquid it may stay at the surface if the agitation is to low. The reason why it stays on the surface is that when a powder is poured into a liquid a fine membrane may occur and keep large quantities of the powder dry. But in some cases a more intensive agitation may not be the solution due to the increased share forces.

2.2.1 Sedimentation

When solids are introduced into a liquid the settling time will be different depending on the added amount. The sedimentation is considered as free for solid’s concentrations below about 30-40% and free means that the particles can settle in the tank without bouncing to much into each other. When the concentration of solids is about 50% the sedimentation becomes hindered as the particles can not settle down without bouncing continuously against each other. Collisions between the particles increase settling time. The boundary between the levels varies depending on particle sizes and shape of the solids. This mixture of liquid and particles with hindered sedimentation is called slurry and the viscosity goes down with high shearing.

For low and increasing concentrations of solids the relative power need for suspension increases almost linearly. (fig 2.1) When reaching concentrations around 50% the transition to the hindered part of sedimentation occurs. The power need is reduced as a result of the amount of particles in the mixture that bounces against each other and results in increased buoyancy. When the amount of particles increases even more, needed power increases again mostly because the viscosity and the density increases.

Fig 2.1 Power need for different concentrations of dry solids.

2.2.3 Degree of suspension

Scanpump defines three different levels of suspension “DoS” (fig 2.2). For DoS 1 (On- bottom motion) the homogeneity of the mixture is about 30 %. For DoS 2 (Complete of- bottom suspension) the homogeneity is 40-60% and the needed power is still moderate. DoS 3 (Uniform suspension) has homogeneity around 80-90% and the relative power needed is twice the power needed for DoS 2 is five times higher than the first DoS. To homogenize the mixture more than third DoS is just wasteful as the power needed for a small improvement of the homogeneity is so great.

Fig 2.2 Homogeneity as function of relative power to get different degrees of suspension

2.2.4 Particle motion in liquid

A particle is only moving in a liquid under influence of an external force. There are also counter forces hindering the particle movement. Buoyant force is trying to lift the particle parallel towards the opposite direction to the external force. The drag force (eq 2.4) appears when there is a liquid motion towards the particle and tries to stop the movement.

For gravitation as external force:

du m −−= FFF (Eq 2.1) dt Dbe m = Particle mass (Kg) u = Velocity (m/s)

Fe = External force (N) = mae (Eq 2.2)

ρam e Fb = Buoyant force (N) = (Eq 2.3) ρ p

2 ρAuC pod FD = Drag force (N) = (Eq 2.4) 2

2 ae = particle acceleration caused by external force (m/s ) 3 ρ p = particle density (kg/m ) 2 Ap = projected particle area (m ) u0 = velocity of approaching stream (m/s) CD = drag coefficient

Combining (eq 2.1) - (eq 2.4) =>

2 2 du ρae D 0 AuC p p − ρρρ D 0 ρAuC p => ae −−= = ae − (Eq 2.5) dt ρ p 2m ρ p 2m

2 When a particle is forced into motion by a gravitational force, ae = g ≈ 9.81 (m/s ), the eq 2.6 will look like:

du − ρρ 2 ρAuC = g p − D 0 p (Eq 2.6) dt ρ p 2m

This equation is considering particle acceleration. The acceleration decreases and totally stops when the particle reaches a speed that is the highest possible with the given forces acting on the particle, ut = terminal velocity (m/s). To get the velocity in the calculations the particle acceleration has to be set to du/dt = 0 and the new equation gives the speed when gravitational force is acting on the particle (eq 2.7).

⎧du ⎫ p − ρρ )(2 mg ⎨ ⎬ = 0 => ut = (Eq 2.7) ⎩ dt ⎭ CA Dpp ρρ

A spherical particle gives a terminal velocity equation under influence of the gravitational forces:

p − ρρ )(4 Dg p ut = (Eq 2.8) 3CD ρ

2.3 Solid dispersion

Solid dispersion is a process in which large particles are broken down into smaller ones. The process needs high shear forces, the impeller speed is often high. Turbines are preferred because they produce the needed high shear forces, see chapter 8.

2.4 Gas dispersion

Gases mix with liquids by two mechanisms, diffusion and dispersion. Diffusion is a natural process of minimizing the concentration gradient and occurs through the contact surface between the gas and the fluid. Dispersing the gas into small bubbles and into the whole volume makes the diffusion process a lot faster due to increased contact area.

Radial pumping impellers are used usually to disperse gases in fluids. The most well known is the Rushton turbine, RFT, see chapter 8. However RFT might not be the best choice for gas dispersion because gassed gas is captured in cavities behind the turbine blades and this phenomenon reduces both the needed effect and the mixing efficiency. To deal with this problem the impeller must be either over dimensioned considering effect and torque or the motor must have two speeds, one for when gas is being added and one when not. To avoid these problems Scanpump uses SRGT, see chapter 8) with curved blades which eliminate the problem of gas cavities thus ensuring stable power usage and mixing effect with a good gas transfer. To describe the gas transfer to the liquid Kla is used. Kla is the transfer coefficient between gas and liquid and reveals how fast the transfer between the phases will occur.

G ak = (Eq 2.9) L ΔcV

A a ≡ V

G: mass flow (kg/s) A: interfacial area (m2) a: interfacial area per unit volume (1/m) kL: mass transfer coefficient (m/s) kLa: liquid side mass transfer coefficient (1/s) c: concentration (g/cm3) V: liquid volume (m3)

2.5 Diffusion

Diffusion is when molecules affected by physical forces move from a higher to a lower concentration and equal out the concentration in the whole volume. The most common is spontaneous diffusion that is happening all the time in nature. Nature always tries to equal the concentration (increase the disorder) even if it takes thousands or millions of years the mixture is always on its way to equilibrium, this might though not be true when an external force is affecting the system (e.g. O2 concentration in the atmosphere).

2.6 Emulsification

Emulsification is the process of distribution of finely divided liquid particles of one liquid (dispersed phase) in another immiscible liquid (continuous phase) (fig 2.3). If the sizes of the particles in the dispersed phase are in range of one nanometre and one micrometer, the mixture is caller colloidal emulsion.

Fig 2.3 Droplets of the dispersed phase in the continuous phase.

Emulsions are common in the industry and the emulsification process can be found in food industry, pharmaceutical industry, oil refinery and several other industries. Some of most common and daily used emulsions are butter and mayonnaise. In butter for example, the dispersed phase is water and the water droplets are surrounded by the continuous lipid phase, it is a so called water-in-oil emulsion.

Emulsions are unstable and thus do not form without energy input in form of e.g. stirring. The emulsification process requires high shear stress and therefore the agitators are usually turbines. Coalescence, the phenomenon when small droplets recombine to form bigger ones, takes place over time as the phases in the emulsion return to the stable state unless there is an energy input. A way to make emulsions more stable by increasing the kinetic stability of the emulsion is to add surface active substances, so called surfactants. These additives can prevent the emulsions from significant changes after creation for long periods of time.

2.7 Fermentation

Fermentation is a very old process and was used to produce wine already thousands of years ago. In modern food industry almost all food preparation use a fermentation process in some way. A big advantage with fermentation is that the use of toxic chemicals can be avoided in many processes. When taking care of waste water the solid organic particles are broken down into harmless dissolvable particles and the liquid can be cleaned and returned into nature, the digested particles (sludge) can be used as fertilizer. There are a lot of parameters that has to be monitored for a well working process, some of the most important ones are oxygen concentration, pH and temperature. Rate of mixing is also important, micro organisms should not get destroyed by high shear forces and at the same time the agitation has to be high enough to spread out the micro organisms in the tank maximizing the contact area with the organic substances. Even one failing parameter is enough to make the whole process unsuccessful. A build up of a new fermentation process is often very difficult because all fermentation plants are unique. Good know how from earlier work is essential for a fast and easy build up. Traditions in the industry make it hard to implement new improved equipment into the fermentation processes.

3. Rheology

This chapter explains some of the corner stones of rheology, study of the deformation and flow of liquids under the influence of applied shear stress.

Viscum is the Latin word for mistletoe and the plant is found in warmer parts of Europe, Asia, Africa and Australia. A viscous glue can be made out of mistletoe berries and that is where the word viscosity origin from.

In science viscosity is a measure of a liquids internal resistance to deformation under shear stress, such as pouring or mixing, in other words, resistance to flow. Fluids resist the relative motion of objects through them as well as to the motion of layers within them.

A common way to illustrate the viscosity is by having two plates move relative each other, one plate being stationary and the other moving parallel to the stationary one at a constant speed u, in the direction of the x-axis. The movement sets the fluid between the plates in motion. This motion produces a velocity gradient in the liquid as well as shear stress, τ. A differential velocity gradient perpendicular to the direction of the flow is thus defined by dux/dy (fig 3.1).

Fig 3.1 Illustration of viscosity

Isaac Newton postulated that, the shear stress, τ, for straight, parallel and uniform flow, between layers is proportional to the velocity gradient, ∂u/∂y, in the direction perpendicular to the layers.

∂u = μτ (Eq. 3.1) ∂y

The constant μ here is known as the viscosity, and has SI physical unit pascal-second ( ⋅ sPa ). The fluids for which this equation is valid are called Newtonian fluids. For these fluids the viscosity changes with temperature and pressure, but it is not affected by shear stress nor velocity gradient

Fluids which do not have constant viscosity are called non-Newtonian fluids (fig 3.2),(fig 3.3) and can not be described with classical theories, the study of these fluids is rather rheometry then rheology i.e. rather empiric then theoretic. Viscosity for these fluids changes, depending on the applied shear stress. Non-Newtonian fluids are classified by their rheological behaviour into five classes: pseudoplastic, dilitant, viscoelastic, thixotropic and rhepectic.

The governing formula is:

n−1 ⎛ du ⎞ μ = k⎜ ⎟ (Eq. 3.2) ⎝ dy ⎠

k is a constant called consistency index and n is the flow behaviour index

Most of non-Newtonian liquids are pseudoplastic, n smaller than 1. For these liquids the viscosity is reduced by shearing. This is the case for e.g. toothpaste and paint where the solid particles in the dispersion, under shear stress, break down into individual particles, which now orientate in the flow direction i.e. the liquid becomes less resistant to flowing.

In dilitant liquids the viscosity is increased by applied shear stress, n larger than 1. Some examples of fluids with such behaviour are starch slurries in water, sand and quick sand. What happens in such liquids when shear stress is applied is that the particles in the liquid are pressed apart which leads to formation of cavities that make the liquid less flowing.

Fig 3.2 Illustrates the behaviour of the viscosity, when the increases, for two Newtonian liquids with different viscosity (1) and (2) and two non-Newtonian ones, one of pseudoplastic (4) and one of dilitant (3) class.

Fig 3.3 Illustrates viscosity in logarithmic scale for pseudoplastic, dilitant and Newtonian liquids.

In some liquids the behaviour of the viscosity not only depends on the present temperature and shear rate, but also on earlier applied shear rates and temperatures. The applied shear rate changes the liquids structure and in case of thixotropic and rheopectic liquids the structure of the liquid does not return to the earlier state when shear rate is decreased (fig 3.4). Pseudoplastic liquids with this kind of behaviour are called thixotropic and the liquids for which the viscosity increase with the increased shear rate, dilitant, are referred to as rheopectic.

Fig 3.4 Illustrates the behaviour of thixotropic (1) and rheopectic (2) fluids when the shear rate changes over time.

4. Dimensionless numbers

4.1 Reynolds number

Reynolds performed his classical experiment in 1883. Reynolds used a glass tube where water flow could be regulated and black dye was injected trough a nozzle (fig 4.1). The dye was flowing through the pipe in a straight line and the flow was what we call laminar. Then the flow was gradually increased and at a certain point the dye flow pattern changed dramatically, the flow was now sinusoid or as we call it turbulent. Reynolds postulated a dimensionless number (eq 4.1) that defines whether a flow is laminar or turbulent, this number was later named Reynolds number, Re.

Fig 4.1 Reynolds experiment. A. Dye at laminar flow B. Dye at turbulent flow

Vd ρ Re = (Eq 4.1) Pipe μ

d = Pipe diameter (m) V = Liquid velocity (m/s) ρ = Density (Kg/m3) μ = Viscosity (Pas)

For Reynolds numbers, Re < 2100, viscous forces keep the flow laminar in the pipe. For Re > 4000, inertial forces dominate and the flow is turbulent. The region between 2100 < Re < 4000 is called transition area, nor laminar or turbulent flow occur here but depending on other factors besides the variables in Reynolds equation both turbulent and laminar tendencies can be observed for short moments.

When calculating Reynolds number in tanks the classical Reynolds number (eq 4.1) can not be used. Agitator Reynolds number describes the flow near the impeller when agitating in a tank and is what, from here on, will be referred to as Reynolds number, Re.

The equation below (eq 4.2) is for calculating agitator Reynolds number for Newtonian liquids.

ρND 2 Re = (Eq 4.2) Agitator μ

D = Impeller diameter (m)

For Reynolds number Re<10 the flow is laminar and turbulent when Re>10000. (McCabe, Unit operations of chemical engineering, 1993).

EXAMPLES If agitating with an impeller that is 2 meter in diameter in two different viscosities the Reynolds number are as follows.

Example a. Rotational speed 2 rps in water. Water: ( ρ =1000 Kg/m3 , μ = 1 mPas )

ρND 2 ⋅⋅ 221000 2 (eq 4.2) -> Re == = 8000000 > 10000= Turbulent (Fig 4.2b). Agitator μ ⋅101 −3

Example b. Rotational speed 2 rps in starch syrup. Starch syrup: (ρ = 1500 Kg/m3, μ = 100000 mPas )

ρND 2 ⋅⋅ 221500 2 (eq 4.2) -> Re == <= 10000120 = Laminar (Fig 4.2a.) Agitator μ ⋅10100000 −3

Fig 4.2a. Laminar flow. b. Turbulent flow.

When agitating non-Newtonian liquids, equation (eq 4.2) is not usable for calculating Reynolds number. That is because viscosity changes with shear rate (fig 4.3) and the stresses differ a lot in different places in the tank. Apparent viscosity (eq 3.2) has to be used in the main equation for Reynolds number.

Fig 4.3 Sugar syrup is a Newtonian liquid because it has the same viscosity no matter the shear stress. When ketchup is exposed to shear stress the viscosity changes and that behaviour is characteristic for Non-Newtonian liquids.

The non-Newtonian fluids discussed in this book are following the so called power law and these liquids are called power liquids. That means that K’, n’ are constants for moderate shear forces, see eq 3.2.

ρND 2 (eq 4.2) + (eq 3.2) -> Re Agitator = n −1' (Eq 4.3) ⎛ du ⎞ K'⎜ ⎟ ⎝ dy ⎠

The velocity gradient differs a lot in an agitated tank and an approximation has to be done in order to be able to calculate the equation. It has been shown that average shear rate in a tank is depends to great extent on the impeller speed. Approximation (eq 4.4) gives satisfactory results in most pseudoplastic liquids for straight bladed turbines.

du = 11n , (Unit operations of chemical engineering series, McCabe, 1993) (Eq 4.4) dy

ρND 2 ρ −n DN 2'2 (eq 4.3) + (eq 4.4) -> Re Agitator = = (Eq 4.5) ()11' nK n −1' K 11' n −1'

4.2 Power number (Newton number)

Power number (eq 4.6) is commonly used for different scale up operations and is the relation between resistance force and inertia force. As an example power number can be used to make a correlations log-log plot for a specific impeller and baffle configuration by plotting “power number vs. Reynolds number” (fig 4.3). For a unique system it can be seen for what Reynolds number the flow will be laminar, transitional or turbulent. Differences for an unbaffled and baffled tank can also be seen in the graph.

Sir Isaac Newton's First Law of Motion (Description of inertia), “Every body perseveres in its state of being at rest or of moving uniformly straight ahead, except insofar as it is compelled to change its state by forces impressed.”

P N = (Power number) (Eq 4.6) p ρ DN 53

ρ: Fluid density (Kg/m3) P: Power (W) N = Rotational speed (1/s) D = Impeller diameter (m)

Fig 4.3 Typical Power curves for Re < 10000, baffled and unbaffled agitator tank.

4.3 Scaba pumping number

Scaba pumping number (eq 4.10) is the liquid speed far away from the impeller and is proportional to the pumping capacity divided by the diameter of the propeller

= ρQvF 0 (Eq 4.7)

F: Momentum, Kg/s

⎛ D 2 ⎞ ⎜ ⎟ = vQ 0 ⎜π ⎟ ⎝ 4 ⎠ (Eq 4.8)

vo: Outgoing speed (m/s) Q: Volumetric flow rate (m3/s)

Because the momentum is conserved in the cone below the impeller (fig 4.4) the approximations (eq 4.9) can be done. Liquid velocity is approximately the same at the blade tip as a bit away. The approximation states that impeller diameter (D) is the same as the flow cone diameter (T), (fig 4.4).

D 2 T 2 Combining (eq 4.7) + (eq 4.8) => = vF 2 ∝ ρπρ v 2 (Eq 4.9) o x 44 vx: Axial velocity at distance x. (m/s) T : Flow “cone” diameter at distance x. (m)

Fig 4.4 Shows the flow cone when agitating.

(eq 4.9) => {to see all operation see appendix A.} =>

Q => v ∝ (Scaba pumping number) (Eq 4.10) x D

4.4 Scaba number & flow number

Scaba number (eq 4.14) measures the agitator’s capability to make liquid flow far away from the impeller in relation to power input. When comparing different agitators it should be done by making sure to have the same Scaba number instead of keeping the same speed for different impellers. Then, based upon the Scaba number, make calculations to find out the best solution with different sizes or speeds.

(eq 4.6) is rearranged to (eq 4.11) {se appendix A for full operations}

2 P ND = 4.0 (Eq 4.11) ⎛ 1 ⎞ ⎜ ρNN 2 ⎟ ⎜ p ⎟ ⎝ ⎠

2 q NDN vx = 1 (Eq 4.12) V 3

Nq: Flow number is the discharge flow from the blade tip on the impeller or pumping ability.

Q N = (Eq 4.13) q ND 3

q PN ⎛ P ⎞ (eq 4.11) + (eq 4.12) => vx = => vx ∝ ⎜ ⎟ => 1 4.0 ⎜ ⎟ 1 ⎛ ⎞ ⎝ N ⎠ 3 ⎜ ρNNV 2 ⎟ ⎜ p ⎟ ⎝ ⎠

⎛ P ⎞ => N sc = ⎜ ⎟ (Scaba number) (Eq 4.14) ⎝ N ⎠

The Scaba number can not be used to compare different impellers because the variables in the

N q N q main equation 4.0 are different between different impellers. But 4.0 can be used as an N p N p efficiency value for impellers.

Example: Assume that an agitator uses 1kW and rotates 1rps. Another agitator rotates 2rps and we wish to get the same process result with the agitator going twice the speed.

⎛ P ⎞ ⎛ 1kW ⎞ ⎛ P ⎞ (Eq 4.14) => N = ⎜ ⎟ => ⎜ ⎟ = ⎜ ⎟ => = 4.1 kWP sc ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ N ⎠ ⎝ 1rps ⎠ ⎝ 2rps ⎠

Required power is 40% higher to get the same degree of agitation when using the higher rotational speed 2rps instead of 1rps rotational speed.

4.4 Degree of agitation

There are different theories how to dimension an agitator. Some use specific power (W/m3) for the scale up in relations with tank shape. Often this gives an oversized agitator that will use a lot more energy than needed. Some use the impellers pumping capacity to scale up the agitator and often end up with an undersized agitator with undesired process capabilities. Scaba found a better way to calculate agitation in a tank by using the velocity in the tank. The speed at the bottom of the tank is always higher than at the surface, therefore it is reliable to measure the surface speed and scale up the agitator according to that. 10 degrees of agitation (DA) are defined and the description of processes and where the specific DA are used can be seen below (table 4.1)

Table 4.1 Describing degree of agitation, Relative power is the power between the first and the preferred degree of agitation.

4.7 Froude number

The Froude number is the ratio of the internal to gravitational forces in the flow. It can be used to calculate the resistance of objects moving through fluids and compare objects of different sizes. This number is named after William Froude, 1810-1879, who was an English engineer educated in Oxford. Froude number can also be interpreted as the ratio between the speed of the surface wave and the speed of the mean flow, implying that if the Froudes

number is greater then one the flow is supercritical and the internal forces are governing the behaviour of the flow.

The dimensionless Froude number is defined by:

v Fn = gLWL (Eq 4.15)

v = speed (m/s) g = gravity acceleration constant (m/s2) LWL = waterline length. (m)

When used in the context of the Boussinesq approximation in fluid dynamics Froude number is defined as:

u Fn = (Eq 4.16) ′hg

and is called densimetric Froude number. u = Speed (m/s) g′ = Reduced gravity (m/s2) h = Representative length scale.(m)

For calculating the Froude number in agitated tanks Scanpump uses a correlation more suitable for that purpose:

u 2 Fn = (Eq 4.17) gd

u = speed (m/s) g = gravity acceleration constant (m/s2) d = impeller diameter (m)

5. Liquid motion

5.1 Mixing Time The time that it takes for a substance to mix to a desired mixedness with a liquid is called mixing time. For a stirred tank with a single phase liquid the mixing time is from that moment a tracer is introduced into the tank until desired mixedness is achieved. A common way to measure mixedness is by using coefficient of variation, CoV, which is a measure of fluctuations in concentration.

N _ 1 2 ∑ i − CC )( N i=1 CoV = _ (Eq 5.1) C

C = Concentration _ C = mean concentration

Mixedness is expressed as − CoV ⋅100)1( . Thus a value of CoV of e.g. 0.1 corresponds to 90% mixedness and 0.01 to 99% mixedness. Worth to note in order to avoid confusion is that same mixedness can be achieved at different concentrations.

Thus it is not only important to decide the desired concentration but also to be aware of the fluctuations of the concentration and choose appropriate maximum of allowed fluctuations e.g. mixedness (fig 5.1). It is important to make sure that the introduction of the tracer material was made in the same way and place when comparing different results. The location of the detector is also crucial when comparing mixing times (fig 5.2).

Fig 5.1 showing concentration fluctuations over time and desired maximum deviation from the equilibrium.

Fig 5.2 shows tank setup for measuring mixing time.

5.2 Caverns The first time the term cavern was used was in 1975 (Wichterle and Wein) to describe the behaviour around the impeller for a pseudoplastic fluid. The behaviour of non-newtonian liquids is poorly understood and a lot of research is in progress in this particular area.

The cavern is the agitated volume that is surrounded by stagnant fluid. For a pseudoplastic liquid the cavern where the mixing takes place is located closely around the impeller where the applied shear rate is high (fig 5.3).

Fig 5.3 Showing where caverns occur in pseudoplastic liquids.

Stagnant fluid means that there is no material exchange in the fluid other than by diffusion. Observations have been done with dye that has been injected into a cavern and showed that there was no dye exchange for hours with constant impeller speed between the cavern and the stagnant area. The cavern surface is located where the liquids shear rate is equal to the shear stress applied by the agitator.

Amanullah proposed in 1998 a model for calculating cavern diameter for non-newtonian liquids with axial-flow impellers (eq 5.2)

n 1 ()n−2 ⎡ ()n−2 ⎤ ⎛ 2 ⎞⎛ 4π 2 K ⎞ n = ⎢4vD ⎜ ⎟ + b n ⎥ (Eq 5.2) c ⎢ c ⎜ ⎟⎜ ⎟ ⎥ ⎝ n −1⎠⎝ Ft ⎠ ⎣⎢ ⎦⎥

Dc = Cavern diameter. [m] vc = Fluid velocity at the cavern boundary. [m/s] n = Flow behaviour index. Ft = Total impeller force. [N] K = Flow consistency coefficient. b = (Vessel diameter/4), Cavern model parameter. [m]

To avoid stagnant regions in pseudoplastic liquids it is possible to use several impellers to make sure that the whole tank gets agitated (fig 5.4).

Fig 5.4 Two impellers in pseudo plastic liquid.

6. Scaba modular system

Scaba has a philosophy to reach the process goals, keep energy consumption as low as possible and to ensure the agitator is mechanically stabile. The philosophy requires that there is a great variation of options when considering the parts used to agitate the tank contents. Therefore the Scaba modular system where different modules can be combined is advantageous (fig 6.1). Scanpumps knowledge together with the great variety of options when dimensioning agitators is a big advantage. For a complete list of modular system combinations available see appendix C. Top and side mounted agitator parts has same housings so spare parts needed on a site can be minimized if numerous Scanpump agitators are used. Another great feature is that maintains work can be done on site without emptying the tank, the agitators are especially designed for that.

Fig 6.1 Top mounted agitator

6.1 Motor

Motors are particularly important when dimensioning the agitator so the energy consumption is low and the motor manages to do the process work without overheating. Standard motors are available between 0.12 kW- 250kW. Electric motors is the most used motor type but there are hydraulic and pneumatic motors too if that should be a requirement. The motor manufacturers that Scanpump uses are ABB, SEW and NORD.

6.2 Gear unit

The gear unit is used to change gear down the rotational speed and is the part that will handle torque from the impeller shaft. When the rotational speed is changed down it gives a stronger agitator when it comes to torque.

When the gear is dimensioned “service factor” is used. Service factor determines the time a gear is supposed to work within a margin of error (fig 6.2). A value between 1.25 and 2 is usually chosen. 1.0 means that the gear only is able to withstand forces exactly defined by the manufactor. 2.0 means that the gear can take forces twice as big as defined. This means that the gear is over dimensioned, will work longer and be more reliable but at expense of the economical aspect.

Fig 6.2 Schematic graph for estimated life time for a motor.

6.3 Bearing housing

The bearing house takes up radial forces generated by the impeller. The axial length of the module bearing is what decides the amount of radial force the bearing can withstand and also the value of the critical speed. Radial forces should always be calculated for, especially when using long shafts or side mounted agitators that are known to create big radial forces that can fluctuate a lot.

The bearing absorbs axial forces that propellers generate and it also carries the weight of the shaft and impeller.

6.4 Seal housing

Scanpumps modular system approach makes it possible to have numerous options when dimensioning an agitator. For example if the process is known to create big axial forces it is a good idea to use bigger bearings and that is possible without changing the whole construction, just choose a bigger bearing and keep the smaller seal housing. This is possible when using the standardized module system. The system also makes it possible to use the same seal and bearing housings no matter if the agitator is top or side mounted (fig 6.3).

Fig 6.3 Scaba’s standardized module system works on both top and side mounted agitators.

6. 5 Shaft seals

Shaft seals make sure to seal the shaft from letting anything unwanted from coming out of the tank, also to make sure no dirt comes into the tank. This is very important when working with toxic or explosive gases and liquids. There are different kinds of seals for different processes. Some of the most common seals are described below. Some of the below described seals only work when they are top mounted and some can be used both as top and side mounted seals.

6.5.1 Stuffing box (S)

This all-round seal is a simple and heavy duty shaft seal (fig 6.4). The strings of seal material are put under pressure to make sure it is tight around the shaft. The amount of strings depends on the process where the stuffing box is used. The stuffing box is not a 100% safe seal and some gas, if the seal is over liquid, will leak out, if under surface, some liquid will flush out and can work as lubricant. The seal works trough contact with the shaft and frequent adjustments and services are necessary to be sure to avoid failure when the seal wears out. This seal can be used in both top and side mounted applications.

Fig 6.4 Stuffing box

6.5.2 Lip seal

Lip seals are the least complex seals used for agitators. The seal is used to make sure no dirt gets in to the tank. The lip seal cannot seal a pressurised tank over 0.5 bar. There are different kinds of lip seals depending on usage. Radial lip seal is a common lip seal used for normal conditions (fig 6.5), it is made up by an elastic material that lies against the shaft. Hygienic lip seals have to be used when working with processes that require a high hygienic standard (fig 6.6). Lip seals can only be used on top mounted agitators.

Fig 6.5 TS, Radial lip seal.

Fig 6.6 TH, Hygienical lip seal.

6.5.3 Mechanical seals (Single Mechanical, Double Mechanical) Mechanical seals (fig 6.7) are more advanced than the seals described earlier and replace many stuffing boxes and lip seals because they can usually run longer periods without supervision or maintenance.

Fig 6.7 Mechanical seal (single).

There are two very essential parts in a mechanical seal. First there is the moving part that is assembled on the shaft and then there is the stationary part assembled to the tank. These two parts glide against each other and in order to keep the wear at a low level hydrodynamic lubrication is used (fig 6.8). The moving part is usually the softer part and will wear faster, it has to be changed after some time. For tanks under pressure mechanical seals are preferred. A double mechanical seal means that a second seal is used and lubrication is pressurised between the first and second seal, it is called fluid barrier and is the only thing that can leak out or in trough the seal when a double mechanical seal is used.

Fig 6.8 Hydrodynamic lubrication

6.5.4 Labyrinth seal

Labyrinth seals are suited for low pressurised tanks where smelly or dangerous gases are kept inside the tank (fig 6.9). The seal material is a continuously supplied liquid, it keeps the friction low between the seal and the shaft it also ensures no leakage can occur. Maximal pressure for a labyrinth seal is 0.5 bars as standard but it can be changed by using a higher column of water that withstands higher pressure.

Fig 6.9 Labyrinth seal

6.6 Shafts

It is important to calculate critical speed, see chapter 9.2, when dimensioning shafts the frequencies create uncontrolled oscillations. Hollow shafts can be used to reduce weight and increase the critical speed, which make it possible to use longer shafts at higher speeds.

When building large tanks that need shafts that are several meters long it is difficult to use shaft that are in one peace. Instead the shaft is shipped in parts and assembled on site. Another great advantage with a shaft in parts is that these can vary in diameter if needed.

6.7 Couplings

There are several different couplings on the market. The most commonly used are described in this chapter.

6.7.1 Flange couplings

Flange coupling are the most used couplings (fig 6.10). When assembling the shaft the outer part is heated up before the inner part is inserted in place and the two parts are screwed together. When the outer part cools down it shrinks and the coupling is tightly assembled.

Fig 6.10 Flange coupling

6.7.2 Threaded coupling

Threaded couplings are used when working with hygienic processes. It is important to make sure the rotation always is against the threads otherwise the shaft parts might come loose. There is an O-ring in the coupling that is squeezed tight so no liquid can get to the threads (fig 6.11).

Fig 6.11 Threaded coupling

6.8 Bottom steady bearing

When using long shafts it can be convenient to use a guide ring (fig 6.12) or a bottom steady bearing (fig 6.13) that will take some of the radial forces that are generated. The guide ring/steady bearing are assembled on the tank bottom. The bottom steady bearing increases the critical speed and makes it possible to use smaller shaft diameters.

Fig 6.12 Guide ring

Fig 6.13 Bottom steady bearing

7. Tanks

7.1 Tank geometry

Agitator tanks can be of various sizes and shapes which give different stirring characteristics. The main purpose for the tank is to preserve a fluid as long as needed. The second purpose is to function as a stirring vessel. This is where the tank characteristics are of great concern when dimensioning stirring equipment for processes. For smaller tanks the cylindrical tank shape is used frequently, for bigger processes rectangular tanks that are moulded in the ground are more popular because they are cheaper to build. The rectangular tank shape has a big disadvantage and that is the sharp bottom corners where particles can sediment. Common solutions are to use fillets (fig 7.1) which eliminate the sharp corners or to use a more energy consuming stirring equipment that force the particles into motion. The later is though the least economical solution, fillets are recommended.

The tank geometry should always be taken in concern when dimensioning stirring equipment. A low and wide tank is better for agitation than a tall and narrow tank when considering using one impeller. Desired tank geometry is “liquid height”/ “tank diameter” = 0.8 for most one- impelled processes (fig 7.2). In agitation literature the preferred number usually is 1 but Scanpumps own research have shown that that 0.8 is the best factor (fig 7.3). At many work facilities though, the ground space is limited and saving space is more important than running the agitation at lowest possible cost.

Fig 7.1 Fillets used for better agitation.

Fig 7.2 Tank geometry H/D.

Fig 7.3 Graph over the relations H/D and Relative power.

7.2 Baffles

Vortexes may be created when stirring at high speeds and are not desired because they tend to suck down air into the liquid changing the fluid behaviour which can be devastating for the process and in the worst case damage the stirrer. Another problem in stirring processes can be that the impeller makes the entire liquid volume in the tank to swirl around as a homogenous body and that means that the agitation is not as efficient as it could be and pumping goes down. Flat sheets called baffles are the solution (fig 7.4). Baffles create shear forces stopping the homogenous mass swirl in the tank and the energy is used for mixing the fluid instead of just moving it around. The most common way in the industry to calculate baffle size is T/10 in Europe and T/12 in America (fig 7.4). Instead of using T/10 Scanpump calculate the baffle size and the clearing towards the tank wall with Reynolds number and uses tables which give a more accurate baffle size that save energy. If the fluid being mixed has a very high viscosity the internal shear forces make it pointless to use baffles. In rectangular tanks it is common not to use baffles as the rectangular tanks have natural baffles, the sharp corners. In rare cases where the mixing speed is very high it can be necessary to use baffles in rectangular tanks as well.

H Hv

S B S T

Fig 7.4 Tank with Baffles. T: tank diameter H: baffle height B: baffle width Hv: liquid height S: baffle clearing towards tank wall

A so called “fully equipped” tank is equipped with 4 baffles. Any more baffles would not do any difference for the process. In some cases the process only needs 1, 2 or 3 baffles for acceptable result. Scanpump has found that a top mounted “off centre” assembly with one baffle (fig 7.5) generates same amount of forces on the stirrer shaft as a top mounted “in centre” stirrer (fig 7.4) with 4 baffles. Note that the agitation is not the same and when using an “off centre” agitator there could be sedimentation built up in the opposite corner from the stirrer. In some processes bottom installed baffles is all that is needed, these are dimensioned in the same way as the wall mounted baffles. If it is undesired to use baffles in the process, the stirrer can be mounted at an angle to the tank’s axis (fig 7.6) but the uneven forces generated on the shaft has to be calculated for. A reason not use standard baffles can be hygienic processes for example. Hygienic baffles can be used when needed and are welded towards the tank so that there are no spaces where bacteria can start to grow and they are easy to clean (fig 7.7).

Fig 7.5 top mounted “off centre” with one baffle.

Fig 7.6 Angle mounted stirrer.

Fig 7.7 Hygienic baffles, tank seen from above.

8. Impellers

Propellers are made for axial flow (fig 8.1), which means that the liquid is sucked in from one axial side of the propeller and thrusted out in a straight line at the other side. A turbine sucks in the liquid from axial directions and throws the fluid out in radial directions (fig 8.2).

Fig 8.1 Axial flow (SHP) Fig 8.2 Radial flow (Rushton)

8.1 Turbines

Turbines are usually used in processes that require high shear stress, usually when one or more of media to be mixed has/have high viscosity. A turbine sets liquids into radial motion, or if the media has high viscosity we speak of tangential flow (Zlokarnik, stirring 2001). Turbines are usually used for dispersion of liquids and gases.

8.1.1 Rushton turbine

One of the most well known turbines is the so called “Rushton turbine” (fig 8.3). Rushton turbine is a disc supporting 6 blades and is usually used for high speed low viscosity liquids mixing in baffled tanks or is off-centre mounted. It will be referred to as 6RFT. In some literature the Rushton turbine is referred to as DT, disk turbine. This can be misleading since the Rushton turbine is not a disc turbine. The design of the 6RFT is standardized, the blades and the disc can be described in correlations of d, stirrer diameter and D, inside tank diameter. The correlations are: the disc is 2d/3, the blades are d/5 high and d/5 wide. The diameter ratio of the Rushton turbine is given by D/d = 1/5.

Fig 8.3 Rushton turbine, often abbreviated as RT6.

8.1.2 6SRGT

6SRGT is a turbine patented by Scaba AB (fig 8.4). It is, at first sight, much like the Rushton turbine but is, due to its superior design, more stable considering the power imparted to the fluid at moderate to high gas rates.

Fig 8.4 6SRGT

6SRGT has rounded, streamlined blades while the 6RFT has flat blades. This difference is a result of a complex research of the fluid mechanics near the blades. The rounded blades considerably decrease the formation of gas filled cavities behind the blades (fig 8.5) which gives considerably more stable power consumption by the impeller and the power imparted on the fluid is close to constant compared to 6RFT (fig 8.6).

Fig 8.5 Rushton turbine Fig 8.6 6SRGT

When the amount of gas increases in the mixture, the efficiency of a Rushton turbine (RFT) can “dive” as low as to 50% of the initial power output. This happens due to, as mentioned before, the formation of gas cavities behind the turbine blades. Because of the design of the 6SRGT these cavities are minimised and the relative power imparted on the fluid is stable and can be held on a desired level.

Figure 8.7 shows what happens to the relative power when the gas flow increases for Rushton turbine (RFT) and the 6SRGT (SRGT). It is also clear that if the 6RFT satisfy the need, one can choose to install the SRGT2 to work at half the power and still have the same mixing capacity as the RFT turbine. Thus, by installing the SRGT 2, the initial investment can be lower due to the fact that there is no need in double speed motors and excessive power.

Fig. 8.7 Relative power vs. increase gas flow for three different turbines

8.1.3 HD Turbine

HD turbines are used when the process require high shear stress (fig 8.8). The HD turbine can be placed near the bottom to prevent sedimentation and usually run at a high rpm. Placing this turbine near the bottom eliminates the cavern under the turbine i.e. eliminating the problem of bad material transfer between the caverns.

Fig 8.8 HD Turbine

8.2 Propellers

When mixing liquids or liquids are mixed with particles a SHP is suitable in most (95%) of the cases. It is designed to make great amount of flow with as small shear forces as possible, that results in low energy consumption. The SHP is design registered and patentented since 1972 by Scaba.

8.2.1 SHP1&SHP18 SHP1 (fig 8.9) looks like the classical propeller and SHP18 (fig 8.10) is a further development from the classical design made for low viscosity applications and is design registered. Numbers 1 and 18 in the names of the propellers have to do with the propeller diameter and blade curvature.

Fig 8.9 3SHP1 propeller.

Fig 8.10 3SHP18 propeller.

8.2.2 Constant pitch The SHP is designed with thin blades that have low resistance when cutting through the liquid. The patented blade shape has constant radius of curvature and decreased blade angle towards the blade ending (fig 8.11) that pumps the same amount at all radius points of the propeller blade “constant pitch”. The result is better flow far away from the propeller since the axial thrust is more concentrated than many other propellers on the market. All these advantages results in better process results with lower energy costs. A blade can either be welded or bolted to the hub. Bolted blades can be thinner than welded and that keeps the weight down. For hygienic processes welded blades are used.

Fig 8.11 Patented blade design “The tangent on each point of the centre line gives the angle at every distance from the centre of the propeller. This angle is 17 degrees at the blade tip and increase against the centre and gives constant pitch”

8.2.3 Gliding ratio Gliding ratio is the ratio between the force of resistance and the lifting force. That means that the gliding ratio is the necessary power needed for the blade to be pushed through the liquid without making any difference in the mixing process when Reynolds number changes. In the graph (fig 8.12) the Scaba profile has a low gliding ratio and is insensitive to Reynolds number. The Marine profile has a high gliding ratio at low Reynolds numbers but when the viscosity goes down, Reynolds number gets higher and the marine profile starts to work more efficient. The 45 degree flat profile has also almost the same gliding ratio for different Reynolds numbers. In comparison with the Scaba profile it has at least twice as high gliding ratio that gives very high power consumption when compared. The conclusion is that the Scaba profile works very good in many different processes with different Reynolds numbers.

Fig 8.12 Graph over gliding ratio depending on Reynolds number at unchanged propeller speeds.

8.2.4 SHPD

Gentle and low shear agitation in extremely high viscosity liquids is the trademark for SHPD (fig 8.13). It is a double acting propeller that creates a flow downwards in the centre of the propeller and a flow upwards on the edges. The equal share of up and down flow results in no axial forces and makes it possible to use thin blades.

Fig 8.13 2SHPD propeller.

9. Stirrer installation.

9.1 Mounting The best way to mount a stirrer depends on the process and wanted characteristics for the agitation. The stirrer can be mounted either from the top “in centre” (fig 9.1) or top “off centre” (fig 9.2). Side mounted stirrers (fig 9.3) are also common especially for processes where short stirrer shafts are preferred due to high speeds. A good way to make sure no particle get stuck in the tank corner is to use fillets. Angled mounted stirrers are mostly used when stirring food or other hygienic fluids (fig 7.6). In special cases the stirrer is mounted underneath the tank to shorten the stirrer shaft. The way of mounting the stirrer also creates different forces on the stirrer and power consumption will change.

Fig 9.1 Baffled in centre installed stirrer. Fig 9.2 Baffled off centre installed stirrer.

Fig 9.3 Side mounted stirrer with fillet.

9.1.1 Impeller position from wall or bottom

When a stirrer is mounted into a tank it is important to use the right spacing towards the tank wall. The spacing has a big impact on power consumption and end result. If a top mounted stirrer with a propeller is installed too close to the bottom the axial flow propeller will start to work like a radial flow turbine instead. The end result is that the tank is not properly agitated. The system would use a lot of energy that would not be taken care of. (fig 9.5)

When a side mounted stirrer is used the spacing behind the impeller is of great importance. The spacing should not be smaller than 0.5 x D otherwise the propeller start to function as a radial flow turbine and desired rate of mixing will not occur. Spacing from the tank bottom is also of big importance and should be 0.75 x D. If the spacing is smaller a radial force will create bending forces on the shaft. To big spacing will cause sediment to build up on the bottom (fig 9.4).

Fig. 9.4 side mounted agitator tank Fig 9.5 side mounted agitator tank with with measurements. measurements

9.1.2 Number of impellers

A high and narrow agitator tank that does not have a good tank shape factor, Fig 7.3 can make it necessary in some cases to use two or more impellers on the top mounted stirrer shaft to ensure liquid motion in the whole tank. The clearing between the impellers should not be less than one impeller diameter it is also important not to mount the top impeller too near the surface. That would cause vortexes to build up and as mentioned earlier the air sucked into the liquid changes the behaviour of the liquid and in worst case damage the stirrer.

9.2 Self-frequency

Self-frequencies are a phenomenon that all rotating systems have. If the system is exposed to force cycles near the self-frequency, “critical speed” the amplitude of the vibration will build up fast and often cause serious damage to the system. This is because the forces collaborate with motion of the system. All systems have an infinite number of self-frequencies but the first and second are of interest for agitators.

Propellers self frequency is particularly easy to calculate and it should be done to make sure the agitator will work as intended. When a two bladed propeller work with a specific rpm. the self frequency is twice that value. For a three bladed propeller the self frequency is three times the rpm. The designer has to make sure that the specific propeller does not work in the critical area of the agitator.

9.2.1 Over/under critical

If the agitator speed is below the first critical speed the mixer is of under critical design. If the mixer is run over the first critical speed the system is of over critical design. When running the system under or over critically the speed should be under 20% for under critically design and over 20% of the first critical speed for over critically design to have a satisfactory safety margin (fig 9.6). Over critical systems have to pass the first critical speed when starting up or shutting down. Therefore it is important to make sure the passing goes fast and that is sometimes solved by a start/stop sequence that makes sure the passing goes as fast as possible.

Fig 9.6 Graph of critical speeds and blade frequency.

Critical speeds can be calculated in advance to get an estimation of where these are. Today it can easily be done with FEM calculating programs or with the wave equation that was used before super computers were on the market.

Bernoulli-Euler wave equation was used and gives the useful (eq 9.1) that can be used to calculate the resonance frequency of the shaft.

EI ω = ki (Eq 9.1) τ s

ω = Resonance frequency (1/s) ki = wave number (1/m) τs = Weight of the shaft per unit length (Kg/m) EI = Bending stiffness of a shaft where E is the “Modulus of elasticity” that is a material constant (N/m2), I is the “Surface moment of inertia” (m4) and is defined as

= ∫ 2 dArI (Eq 9.2)

r = shaft radius.

For a solid circular shaft the surface moment of inertia is

πr 4 I = (Eq 9.3) 4

And when calculating hollow shafts the moment of inertia is

⎛ π ⎞ 44 = ⎜ ⎟(0 − rrI i ) (Eq 9.4) ⎝ 4 ⎠

r0 = outer cross sectional shaft radius ri = inner cross sectional shaft radius

There are numerous factors that have to be included in the calculations of resonance frequencies for agitators. Some of factors that have to be calculated for are impeller weight, the weight of the couplings and axial length of the bearing housing.

When a mixer is installed up at the site it is easy to make sure the calculations where correct. It is done by pushing the shaft and counting the number of oscillations it makes per minute (fig 9.7). When the first critical speed is obtained it is even easier to calculate the second critical speed because it is 4 times the first critical speed. The self-frequency depends much on the shaft length and stiffness. Another important factor for the self frequency is the rubber bushings and tank top that the stirrer can be installed on. A stirrers is over-critically designed if there are rubber bushings.

Fig 9.7 Push and count the oscillations/min.

10. Wastewater treatment

10.1 Flocculation

Flocculation is the process of aggregation of small particles into flocks. Particles form flocks because of the electromagnetic forces. Surfaces, of particles, with different charges are attracted to each other. In water treatment substances called flocculants are used. Flocculants are chemicals with suitable charge, positive or negative, opposite to that of the particles of the dispersed phase and help to reduce the barriers to aggregation. Some of the used flocculants react with water to form hydroxides which in turn, linked together form long meshes and physically trap small particles into larger flocks. Temperature, salinity and pH are factors that effect the induction of flocculation and influence flocculation rates.

Agitation in this process must be very gentle, with low shear stresses, in order not to break up the formed flocks. It is therefore important to have quantitative measure of the mixing intensity in order to keep the shear stress to the minimum and ensure desirable mixing. Mean velocity gradient, given the symbol G, is the parameter used for this purpose:

P G = μV (Eq. 10.1)

P: power used (W) V: liquid volume (m3) μ : viscosity (Pas).

G-value describes the shear force produced by the impeller acting on the flocks. If the shear stress is too big the flocks will be destroyed by the impeller. Process must be dimensioned to prevent that from happening. To ensure desirable mixing a value Gmax is used. Gmax is defined by:

G = N 3 D 2 max (Eq. 10.2)

N: impeller shaft speed (rps) D: impellers diameter. (m)

However the G-value can not be too low either, that would mean that the volume is not properly mixed and that the chemicals, flocculants or salts, do not reach all the dispersed particles.

The empirically established values of G and Gmax are as follow:

G max ≤ 160

at the impellor and G multiplied by T (the retention time) has to be between 10 000 and 100 000

10000 TG ≤⋅≤ 100000

10.2 Denitrification

Denitrification is an important step in waste water treatment. The goal is to reduce nitrate and nitrite into gaseous nitrogen. Nitrate and nitrite are highly oxidised forms of nitrogen and can be easily consumed by many groups of organism. Not reducing them would lead to consumption of oxygen and entropy in the recipient.

Reduction into nitrogen is done in tree steps. The first two steps are aerobic and require input of oxygen. In the third step the reaction requires an anaerobic environment and has to be concealed into a closed tank. In the first step the sludge is oxidised with bubble columns of air in order to oxidise the organic material, → COC 2 . In the second step nitrification takes place, bacteria converts ammonium ions into nitric ions (Eq. 10.3) and then nitrite is reduced to nitrate (eq. 10.4)

+ `` + 24´ 2 2 ++→+ 42232 HOHNOONH (Eq. 10.3)

= = 2 22 →+ NOONO 3 (Eq. 10.4)

The final step in the process is to reduce nitrate to dinitrogen gas. Bacteria oxidise the added methanol using the nitrate in anaerobic environment and produces dinitrogen (eq. 10.5)

= + 3 +→+ 5244 ONHNO 22 (Eq. 10.5)

In steps two and three agitation is needed in order to mix the added chemicals, keep the process liquid and to prevent sedimentation. The aerating process in step two can however is some cases provide the needed agitation and no further agitators need to be installed. In step three the agitators have to provide mild agitation and maximum of degree two of agitation should be sufficient.

10.3 Digestion

Digestion is the process of anaerobic decomposition of organic substance. At a waste water plant this takes place in a digester (fig. 10.1), a hermetically sealed tank with installed agitators.

Fig. 10.1 Shows a digester with three impellers installed on the shaft.

Products of this process are biogas and soil improving material. The time it takes to decompose waste material varies depending on the temperature in the tank. Higher temperature gives lower residence time but needs a larger energy input. The temperature also depends on the choice of bacteria used in the process. The temperature for so called mesophilic process is 35-40 oС and 55-60 oС for so called thermophilic process. Residence time for the mesophilic process is up to 90 days while it can be less then two weeks for the thermophilic process.

The agitation is important to avoid stagnation and also to ensure good heat transfer. Stable conditions in the digester are important for the efficiency of the process. The upper most propeller, that is smaller then the others installed, is there to break the crust building up at the top of the volume. Mild agitation is required. The digesters are usually very big tanks and several impellers are installed on the shaft to ensure required agitation. However since only a mild agitation is required, the power input is rather small, usually not more then some kilowatts. It is common in the industry to rely on the measure / mW 3 when dimensioning impellers which is not the best approach due to the fact that impellers tend to become over dimensioned, thus unnecessary usage of power. Scanpump has a different approach using degree of agitation to determine power and means of impelling needed. Scanpump´s solutions use less power thus saving a lot of energy in the long run. Scanpump also guaranties wanted retention time and offers customers a so called lithium test after the scale up is complete. This test is based on introducing lithium into the volume to work as a trace element. By following change in the lithium content over a period of time, mixing efficiency can be studied and a residence time is determined.

11. Paper pulp industry

Ancient Egyptians were the first people to make paper-like material, called papyrus. They made the papyrus by pounding the inner part of the papyrus steam into flat sheets. The word paper comes from the word papyrus. Paper as we know it today origin from China from around 100 A.D. Today paper is an important product world wide and the world has become depended of high quality paper. In this chapter the discussion will be about paper pulp and a short description of the paper pulp industry regarding agitation and issues that has to be calculated for. Scanpump can design agitators for all processes in a paper mill.

When making paper the raw material is wood. Different wood have different fibre characteristics determined by the cellulose in the specific wood type. In theory it would be possible to make paper of any vascular plant found in nature. But it is the cellulose in the plant that limits the choices of plants that are suitable for paper making out of an economic view. The woods that are usually used at paper mills are spruce, pine, fir, larch and hemlock. The raw wood that comes to the paper mill also has other substances that are not desirable in paper pulp. The paper mill has to clean the pulp to minimize the amount of other substances to be sure of getting a high quality end product. When the pulp is clean it has to be coloured, bleached or treated in other ways, to gain properties that the process requires for the specific paper type, before letting the pulp into the paper machine.

11.1 Liquid motion in paper pulp

Paper pulp is built up by thin flexible fibres that give the pulp a similar behaviour as Bingham plastic liquids. The non-newtonian behaviour makes the modelling of the process very difficult and a good know how is of great importance. The Bingham plasticity is responsible for the big number of flow regimes that will be found in a paper pulp tank. There can be both laminar and turbulent flows and even stagnant pulp can be found if the agitation level is too low. It is very important to make sure that there is not any stagnant pulp anywhere in the tank for longer periods of time and especially in the tank corners which are the first places where stagnation will occur. The use of fillets makes it easier to avoid stagnation (fig 7.1).

Consistency is one of the most important parameters in paper pulp industry because all equipment is dimensioned in correlation with this parameter. The consistency is the percentage of dry solids by weight in pulp.

There is number of different flow regimes for a specific tank shape (fig 11.1). In front of the propeller there is a so called active volume where the flow is turbulent and the consistency accuracy is very good. Above the active volume the low active volume is found and the flow there is laminar, pulp and water are moving in different layers and do not mix, this can give an irregular consistency in that part of the tank. If the agitation is too low in the tank there is a risk that channelling occurs. Channelling is when unagitated pulp flows through the tank in a channel straight to the outlet and the whole process step is then just a waste of power and expensive products.

Fig 11.1 Liquid motion in paper pulp

To be able to avoid these problems Scaba has defined three different levels of agitation in paper pulp (fig 11.2). The first level is “bottom clean” and the agitation is just strong enough to keep the bottom clean from stagnant pulp; if the tank is very low the active volume can take up the whole tank volume even if the agitation level is “bottom clean”. Normally though it will not give a satisfactory mixing in the tank. In higher tanks there will be a layer of non agitated pulp on the surface that can get bad and start to smell if it stays on the surface too long. This pulp can not be used in the process when it has gone bad. Therefore this level of agitation is rarely used. The next level is “good agitation”, the non agitated zone at the surface is gone. The active volume is now ≈ 60% of total volume. The “good agitation” level is recommended for process steps where the accuracy of the outgoing pulp does not have to be perfect or if the retention time is long. The last level is “very good agitation” and is used in processes that require very good accuracy of the consistency. The active volume is taking up the about ≈ 90% of total volume.

Recommended processes for different levels of agitation in paper pulp 1. Bottom clean: rarely used 2. Good agitation: Storage chests, Pulp Chests, Chests with long retention time (≤ 15minutes) 3. Very good agitation: Blending chests, Machine chests, HD-towers, Bleaching towers, Blow tanks, latency tanks.

Fig 11.2 Three defined levels of agitation in paper pulp

11.2 Dimensioning paper pulp processes

11.2.1 Different types of pulp

When dimensioning a process step in a paper pulp industry it is very important to know the consistency of the pulp and what kind of pulp that will be used. The consequences of a small deviation from the true values will probably result in a greatly over- or underdimensioned process. The importance is obvious when looking at the examples below (fig 11.3).

Examples of the importance to know what the process has to handle: Example 1. If the process is dimensioned for 4% unbleached sulphate soft wood but it turns out that the pulp is 5% instead of 4%. The power needed for successful agitation is around 2 times higher than the process is dimensioned for and we can expect problems with stagnant pulp and maybe even channelling.

Example 2. The process is dimensioned for 5% unbleached sulphate soft wood but it turns out that the process is going to use 5% bleached sulphate soft wood. That means that the process is using about twice as much power than needed. Too high power consumption means that the company using the equipment looses a lot of money.

Fig 11.3 Relative power vs. consistency for different kind of pulps.

11.2.2 Temperature

It is important to make sure that the pulp temperature is included in the calculations when dimensioning agitators. Temperature affects the pulp viscosity and needed power for agitation is lower for higher temperatures (fig 11.4).

Fig 11.4 Relative power demand vs. temperature.

11.3 Paper pulp processes The paper making process is complex, this book will only consider the most common parts that need agitation and briefly explain the processes. For a schematic overview of a complete paper mill see appendix B.

Blending/Mixing chests Blending and mixing chests are used to mix different pulps or chemicals. It is important that there is turbulent motion in the whole tank to minimize mixing time.

Machine chest The machine chest is the last station before the paper machine, it ensures that there is pulp for the paper machine that is of the same consistency level at all times. That requires turbulent motion in the whole tank so the intensity of the agitation is high.

Couch pits The couch pit is where the waste ends up from the paper machine and is returned to the process so as little as possible is spoiled. The agitation is low in the couch pit under normal circumstances. If there is a failure in the paper process the quantity of pulp in the couch pit gets very high fast and the required level of agitation gets higher so the paper can be broken up and returned to the system as pulp.

Pulp Chests Pulp chests are only used as a buffer to make sure there is always pulp continuously fed to the process behind. The agitation requirements in the pulp chest are high because the agitation has to keep the pulp consistency constant.

HD-towers (High Density towers), Bleaching towers, Blow tanks In an HD-tower, bleaching tower or blow tank the pulp is stored at a high concentration and to be able to dilute the pulp the shape of the tank is smaller at the bottom so the agitation will be easier because a smaller volume requires less energy. The consistency of the stored pulp is between 10-20% and is often diluted down to a consistency of 3-6 % before the pulp goes to the next process step. If the pulp is over 20% it is recommended that dilution water is inserted into the pulp higher up in the tank than usual. It is important to get a constant consistency on the outgoing pulp. For that purpose an automatic dilution system makes sure the consistency is right all the time (fig 11.5). To try making this process work without an automatic dilution system is almost impossible and not recommended.

Fig 11.5 High density tower with automatic consistency and dilution control.

12. Appendix

Appendix A.

3 3 = q NDNQ (Pumping Capacity, m /s) (Eq 1)

= ρQvF 0 (Momentum, Kg/s) (Eq 2)

53 = p ρ DNNP (Power, kW) (Eq 3)

Q v0 = (Outgoing speed, m/s) (Eq 4) ⎛ D 2 ⎞ ⎜π ⎟ ⎝ 4 ⎠

⎛ D 2 ⎞ ⎜ ⎟ (eq 4) => = vQ 0 ⎜π ⎟ (Eq 5) ⎝ 4 ⎠

3 q NDN (eq 1) + (eq 2) => v0 = => 0 ∝ q NDNv (Eq 6) ⎛πD 2 ⎞ ⎜ ⎟ ⎝ 4 ⎠

D 2 T 2 (eq 2) + (eq 5) => = vF 2 ∝ ρπρ v 2 (Eq 7) o x 44 vx: Axial velocity at distance x. T : Flow “cone” diameter at distance x.

D D (eq 7) => = vv (T3 ≈ V ≈ Tank volume) => = vv (Eq 8) x 0 T x 0 1 V 3

2 q NDN (eq 6) + (eq 8) => vx = 1 (Eq 9) V 3

3 D q NDN Multiply (eq 9) with => v = and we can simplify with Q => D x 1 DV 3

Q Q => v = => v ∝ (Scaba Pumping number) (Eq 10) x 1 x D DV 3

53 = p ρ DNNP (Eq 11)

1 5.2 2 2 = p ρ()NNDNP

P ND 2 = 4.0 (Eq 12) ⎛ 1 ⎞ ⎜ ρNN 2 ⎟ ⎜ p ⎟ ⎝ ⎠

2 q NDN vx = 1 (Eq 13) V 3

q PN (eq 12) + (eq 13) => vx = => 1 4.0 1 ⎛ ⎞ 3 ⎜ ρNNV 2 ⎟ ⎜ p ⎟ ⎝ ⎠

⎛ P ⎞ => vx ∝ ⎜ ⎟ (Scaba number) (eq 14) ⎝ N ⎠

Q N = (Flow number) (eq 15) q ND 3

Appendix B.

Appendix C

D Direct drive

V, FV, VV: Gearbox drive, flange motor

VVR: Gearbox drive, foot motor and flexible coupling

K: V-belt drive

P: Bearing housing (Pedestal) with two row spherical roller bearings

T: Seal housing

Notation a Interfacial area per unit volume, 1/m 2 ae, g Particle acceleration caused by external force, m/s A Interfacial area, m2 2 Ap Projected particle area, m b Cavern model parameter ” Vessel diameter/4” , m c, C Concentration, g/cm3 C mean concentration, g/cm3 CD Drag coefficient d Pipe diameter, m D Impeller diameter, m Dc Cavern diameter, m Dp Characteristic length, m EI Bending stiffness of shaft, E is “Modulus of elasticity” N/m2, I is “Surface moment of inertia” m4. Fe External force, N Fb Buoyant force, N FD Drag force, N Ft Total impeller force, N g Gravity acceleration constant, m/s2 g´ Reduced gravity m/s2 G Mass flow, Kg/s h Representative length scale, m k k-value ki Wave number, 1/m kLa Liquid side mass transfer coefficient, 1/s K´ Flow consistency index LWL Waterline length, m m Particle mass, Kg n, n´ Flow behaviour index N Rotational speed, 1/s p´ Instant pressure, Pa P Power, W Q Volumetric flow rate, m3/s r Shaft radius, m r0 Outer cross sectional shaft radius, m ri Inner cross sectional shaft radius, m t Time, s T Flow cone diameter at distance x, m Tv Vessel diameter, m u´ Instantantaneous velocity, m/s u0 Velocity of approaching stream, m/s v Speed, m/s v0 Outgoing speed, m/s vx Axial velocity at distance x, m/s

vc Fluid velocity at the cavern boundary, m/s V Volume, m3 V Liquid velocity, m/s

Greek Symbols

3 ρp Particle density, Kg/m ρ Density, Kg/m3 μ Viscosity, m2/s ν Shear stress, Pa ω Resonance frequency, 1/s τs Weight of shaft per unit length, Kg/m