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AGITATION AND MIXING

Many processing operations depend for their success on the effective agitation and mixing of

fluids. Agitation and mixing are not synonymous.

Agitation refers to the induced motion of a material in a specified way, usually in a

circulatory pattern inside some sort of container.

Mixing is the random distribution, into and through one another, of two or more

initially separate phases.

Example, a single homogeneous material, such as tankful of cold water, can be

agitated, but it cannot be mixed until some other material (such as a quantity of hot water or

some powdered solid) is added to it.

PURPOSE OF AGITATION Liquids are agitated for a number of purposes, depending on the objectives of the processing

step. These purposes include

1. Suspending solid particles

2. Blending miscible liquids, for example, methyl alcohol and water

3. Dispersing a gas through the liquid in the form of small bubbles

4. Dispersing a second liquid, immiscible with the first, to form an emulsion or suspension

of fine drops

5. Promoting heat transfer between the liquid and a coil or jacket

Often one agitator serves several purposes at the same time, as in the catalytic

hydrogenation of a liquid. In a hydrogenation vessel, the hydrogen gas is dispersed through

the liquid in which solid particles of catalyst are suspended, with the heat of reaction

simultaneously removed by a cooling coil or jacket.

AGITATED VESSELS Liquids are most often agitated in some kind of tank or vessel, usually cylindrical in form and

with a vertical axis. The top of the vessel may be open to the air, more usually it is closed.

The proportions of the tank vary widely, depending on the nature of the agitation problem. A

standardized design such as that shown in Fig. 1 is applicable in many situations.

The tank bottom is rounded, not flat, to eliminate sharp corners or regions into which

fluid currents would not penetrate. The liquid depth is approximately equal to the diameter of

the tank.

An impeller is mounted on an overhung shaft, that is, a shaft supported from above.

The shaft is driven by a motor, sometimes directly connected to the shaft but more often

connected to it through a speed-reducing gearbox.

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Figure 1 Typical agitation process vessel.

Accessories such as inlet and outlet lines, coils, jackets, and wells for thermometers or other

temperature-measuring devices are usually included.

The impeller causes the liquid to circulate through the vessel and eventually return to the

impeller. Baffles are often included to reduce tangential motion.

IMPELLERS Impellers agitators are divided into two classes. Those that generate currents parallel with the

axis of the impeller shaft are called axial-flow impellers; those that generate currents in a

radial or tangential direction are called radial-flow impellers.

The three main types of impellers for low-to moderate-viscosity liquids are propellers,

turbines, and paddles (high-efficiency impellers). For very viscous liquids, the most widely

used impellers are helical impellers and anchor agitators.

Propellers and pitched blade turbine are axial flow impellers; while paddle and flat

blade, disk flat blade turbines are radial flow mixers.

PROPELLER A propeller is an axial-flow, high-speed impeller for low viscosity liquids. It may be mounted

centrally, off-centre or at an angle to the tank. It is simple and portable.

Small propellers turn at either 1500 or 1750 rpm and larger one turn at 400 to 800

rpm. The direction of rotation is usually chosen to force the liquid downward, and the flow

currents leaving the impeller continue until deflected by the floor of the vessel. The highly

turbulent swirling column of liquid leaving the impeller entrains stagnant liquid as it moves

along. The propeller blades vigorously cut or shear the liquid. Because of the persistence of

the flow currents, propeller agitators are effective in very large vessels.

Inlet

Discharge / outlet valve

Thermowell

Baffle

ImpellerVessel

Liquid

surface

Shaft

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Propellers rarely exceed 18 inch in diameter regardless of the size of the vessel. In a

deep tank two or more propellers may be mounted on the same shaft, usually directing the

liquid in the same direction.

Figure 2 Three-blade marine propeller.

Turbines A simple straight-blade turbine, as shown in Fig. 3 (a) and (b), pushes the liquid radially and

tangentially with almost no vertical motion at the impeller. The currents it generates travel

outward to the vessel wall and then flow either upward or downward. In process vessels they

typically turn at 20 to 150 rpm.

Turbines are very effective over a wide range of viscosities up to 104 cP. Turbines

impellers drive the liquid radially against the wall, where the stream divides into two

portions. One of the portions flows downward to the bottom and then returns to the centre of

impeller from below while other flows upward towards the surface and finally returns to the

impeller from above. Turbines are especially effective in developing radial currents, but with

a baffled vessel they also induce vertical flows. To avoid vortexing and swirling with

turbines, baffles or diffuser ring can be used.

Figure 3 (a) Simple straight-blade turbine; (b) Disc turbine

Standard turbine design A designer of an agitated vessel has a large number of choices in

Type and location of the impeller

The proportions of the vessel

The number and proportions of the baffles, etc.

Each of these decisions affects

Circulation rate of the liquid

The velocity patterns and

(a) (b)

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The power consumed

As a starting point for design in ordinary agitation problems a turbine agitator of the type

shown in Fig. 4 is commonly used.

Figure 4 Measurements of turbine

1

3

a

t

D

D 1

t

H

D

1

12t

J

D

1

3t

E

D

1

5a

W

D

1

4a

L

D

where, Da = diameter of the agitator

Dt = diameter of the tank

H = depth of the liquid

J = thickness of the baffle

E = distance between the bottom of the tank and the agitator

W = width of the agitator blade

L = Length of the agitator blade

The number of baffles is usually 4; the number of impeller blades ranges from 4 to 16

but is generally 6 or 8. Special situations may dictate different proportions from those listed

above.

PADDLES For simple situation, a flat paddle turning on a vertical shaft is used. Paddle agitators with

two or four blades are very common. The blades of these agitators normally extend close to

the tank wall. They are simply pushers and cause the mass to rotate in laminar swirling

motion with practically no radial flow along the paddle blades or any axial flow (vertical

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motion). The circulation is poor and the mixing action is insufficient. The speed of rotation is

very low and is generally between 20 to 50 rpm. For viscosities above 20 Pa s (and up to

25,000 Pa s) the helical-ribbon impeller shown in Fig 5 (a) is more effective. The diameter of

the helix is very close to the inside diameter of the tank, guaranteeing liquid motion all the

way to the tank wall even with very viscous material.

To provide good agitation near the floor of the tank, an anchor impeller, as shown in

Fig. 5 (b), may be used. Because it creates no vertical motion, it is a less effective mixer than

a helical ribbon, but it promotes good heat transfer to or from the vessel wall. For this

purpose both anchors and helical ribbons may be equipped with scrappers that physically

remove liquid from the tank wall.

Figure 5 Impellers for high-viscosity liquids: (a) double-flight helical-ribbon impeller

(b) anchor impeller

FLOW PATTERNS IN AGITATED VESSELS The way a liquid moves in an agitated vessel depends on many things:

The type of impeller

The characteristics of the liquid, especially its viscosity and

The size and proportions of the tank, baffles, and impeller

The liquid velocity at any point in the tank has three components, and the overall flow pattern

in the tank depends on the variations in these three velocity components from point to point.

The three velocity components are

1. The first velocity component is radial and acts in a direction perpendicular to the shaft of

the impeller.

2. The second component is longitudinal and acts in a direction parallel with the shaft.

3. The third component is tangential, or rotational, and acts in a direction tangent to a

circular path around the shaft.

In the usual case of a vertical shaft, the radial and tangential components are in horizontal

plane, and the longitudinal component is vertical.

The radial and longitudinal components are useful and provide the flow necessary for

the mixing action. When the shaft is vertical and centrally located in the tank, the tangential

(a) (b)

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component is generally disadvantageous. The tangential flow follows a circular path around

the shaft and creates a vortex in the liquid, as shown in Fig. 6 for a flat-blade turbine.

Figure 6 Swirling flow pattern with a radial-flow turbine in an unbaffled vessel.

Exactly the same flow pattern would be observed with a pitched-blade turbine or a propeller.

The swirling perpetuates (maintains) stratification at the various levels without providing

longitudinal flow between levels. If solid particles are present, circulatory currents tend to

throw the particles to the outside by centrifugal force; from there they move downward and to

the center of the tank at the bottom. Instead of mixing, its reverse–concentration–occurs.

Since, in circulatory flow, the liquid flows with the direction of motion of the impeller blades,

the relative velocity between the blades and the liquid is reduced, and the power that can be

absorbed by the liquid is limited. In a unbaffled vessel, circulatory flow is induced by all

types of impellers, whether axial flow or radial flow.

If the swirling is strong, the flow pattern in the tank is virtually the same regardless of the

design of the impeller. At high impeller speeds the vortex may be so deep that it reaches the

impeller, and gas from above the liquid is drawn down into the charge. Generally this is

undesirable.

PREVENTION OF SWIRLING AND VORTEX FORMATION There three methods of prevention of swirling and vortex formation, they are

1. Off-centre mounting of the impeller

2. Use of baffles

3. Use of diffuser ring with turbines

Off-centre mounting of the impeller

As shown in the Fig. 7, in small tanks the shaft is moved away from the centreline of the

tank, and then titled in a plane perpendicular to the direction of the move. In larger tanks, the

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agitator may be mounted in the side of the tank, with the shaft in a horizontal plane but at an

angle with a radius.

Figure 7 Flow pattern with off-centre propeller.

Use of baffles

In large tanks with vertical agitators, the preferable method of reducing swirling is to install

baffles, which imped rotational flow without interfering with radial or longitudinal flow. A

simple and effective baffling is attained be installing vertical strips perpendicular to the wall

of the tank. Except in very large tanks, four baffles are sufficient to prevent swirling and

vortex formation. Baffles are not needed at all when µ>10 Pa s. baffles are also not needed

with side-entering, inclined, or off-center propellers.

Once the swirling is stopped, the specific flow pattern in the vessel depends on the

type of impeller. Propellers impellers usually drive the liquid down to the bottom of the tank,

where the stream spreads radially in all directions toward the wall, flows upward along the

wall, and returns to the suction of the propeller from the top. Propellers are used when strong

vertical currents are desired, for example, when heavy solid particles are to be kept in

suspension. They are not ordinarily used when the viscosity of the liquid is greater than about

5 Pa s. Axial flow impellers tend to change their discharge flow pattern from axial flow at

low liquid viscosities to radial flow when the viscosity is very high.

Draft tubes

The return flow to an impeller of any type approaches the impeller from all directions. The

flow to and from a propeller, for example, is essentially similar to the flow of air to and from

a fan operating in a room. In most applications of impeller mixers this is not a limitation, but

when the direction and velocity of flow to the suction of the impeller are to be controlled,

draft tubes are used, as shown in Fig. 8.

These devices may be useful when high shear at the impeller itself is desired, as in the

manufacture of certain emulsions, or where solid particles that tend to float on the surface of

the liquid in the tank are to be dispersed in the liquid. Draft tubes for propellers are mounted

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around the impeller, and those for turbines are mounted immediately above the impeller, draft

tubes add to the fluid friction in the system; and for a given power input, they reduce the rate

of flow, so they are not used unless they are required.

Figure 8 Draft tubes, baffled tank: (a) turbine; (b) propeller

POWER CORRELATIONS To estimate the power required to rotate a given impeller at a given speed, empirical

correlations of power (or power number) with the other variables of the system are needed.

The form of such correlations can be found by dimensional analysis, given the important

measurements of the tank and impeller, the distance of the impeller from the tank floor, the

liquid depth, and the dimensions of the baffles if they are used.

The number and arrangement of the baffles and the number of blades in the impeller must

also be fixed.

The variables that enter the analysis are the important measurements of tank and impeller, the

viscosity µ and the density ρ of the liquid, and the speed n. The acceleration of gravity g must

be considered as a factor in the analysis.

The various linear measurements can all be converted to dimensionless ratios. Called shape

factors, by dividing each by one of their number which is arbitrarily chosen as a basis. The

diameter of the impeller Da and that of the tank Dt are suitable choices for this base

measurement, and the shape factors are calculated by the magnitude of Da or Dt. Let the

shape factors, so defined, be defined by S1, S2, S3,…, Sn. The impeller diameter Da is then also

taken as the measure of the size of the equipment and used as a variable in the analysis.

When the shape factors are temporarily ignored and the liquid is assumed Newtonian, the

power P is a function of the remaining variables, or

( , , , , )aP n D g (1)

Application of the method of dimensional analysis gives the result,

(a) (b)

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2 2

3 5,a a

a

n D n DP

n D g

(2)

By taking account of the shape factors, eq (2) can be written,

2 2

1 23 5, , , ,......,a a

n

a

n D n DPS S S

n D g

(3)

The first dimensional group in eq (2), 3 5. .aP n D , is the power number Np. The second,

2. .an D , is Reynolds number Re; the third, 2. an D g , is the Froude number Fr. Equation

(3) can therefore be written

1 2Re,Fr, , ,.....,p nN S S S (4)

The importance of the dimensionless groups in equation (2), for

power calculation in agitation 1. Reynolds number Re

The impeller tip speed 2 au D n .

2

2Rea aa a

n D Dn D u D

This group is proportional to a Reynolds number calculated from the diameter and

peripheral speed of the impeller. This is the reason for the name of the group. At low

Re<10, viscous flow present throughout the vessel, and at Re>104 the flow is turbulent

everywhere. A transition region exists at intermediate Reynolds numbers.

2. Power number Np

The Power number Np is analogous to a friction factor or drag coefficient. It is

proportional to the ratio of the drag force acting on a unit area of the impeller and the

inertial stress, that is, the flow of momentum associated with the bulk motion of the fluid.

3. Froude number Fr

The Froude number Fr is a measure of the ratio of the inertial stress to the gravitational

force per unit area acting on the fluid. It appears in fluid dynamic situations where there is

significant wave motion on a liquid surface. It is especially important in ship design. It is

not important when baffles are used or when Re<300. Unbaffled vessels are rarely used at

high Reynolds numbers, and hence the Froude number is not included in the following

correlations.

POWER CORRELATIONS FOR SPECIFIC IMPELLERS Typical plots of Np versus Re for baffled tanks fitted with centrally located impellers are

shown in Fig. 9.

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Figure 9 Power number Np versus Reynolds number Re for turbines and high-

efficiency impellers.

The top curve is for a six-blade disk turbine. At high Reynolds numbers the curve levels off

at a power number of 5.8. The curve for the CD-6 concave-blade turbine is similar but levels

off at a value of 2.9. The pitched turbine with four blades set at an angle of 450 draws about

70 percent as much power as the standard turbine at low Re, but only about 20 percent as

much at high Re. The A310 and HE-3 high-efficiency impellers have much lower power

numbers than the turbines, and are usually operated at higher speeds. The power number for

all five impellers is constant when Re>104, and it varies inversely with the Reynolds number

when Re<10.

Power numbers for a marine propeller and a helical ribbon are shown in Fig. 10.

Figure 10 Power number Np versus Reynolds number Re for marine propellers and

helical ribbons.

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For the propeller the power number when Re = 104 is about 50 percent greater in a baffled

tank than in an unbaffled one, but at low Reynolds numbers there is no difference. Baffles are

not used with the helical impeller, and Np decreases rapidly as Re increases. No data are

available for a helical impeller for Re>104, but these impellers are commonly used only at

low Reynolds numbers. Power numbers for an anchor agitator are slightly greater than for a

helical impeller over the entire range of Reynolds numbers.

Calculation of power consumption The power delivered to the liquid is computed from the following equation, after a

relationship for Np is specified.

3 5p

a

PN

n D

(5)

Rearranging eq (5)

3 5

p aP N n D (6)

At low Reynolds numbers, the lines of Np versus Re for both baffled and unbaffled tanks

coincide, and the slope of the line on logarithmic coordinates is –1.

Therefore

Re

Lp

KN (7)

Put eq (7) in eq (6), results in

2 3

L aP K n D (8)

The flow is laminar in this range, and density is no longer a factor. Equations (7) and (8) can

be used when Re is less than 10 (Re<10).

In baffled tanks at Reynolds number larger than about 10,000 (Re>10,000), the power

number is independent of the Reynolds number, and viscosity is not a factor. In this range the

flow is fully turbulent, Np becomes

p TN K (9)

Equation (6) becomes

3 5

T aP K n D (10)

The constant KL varies between 36.5 and 300, and KT varies between 0.28 and 5.75.

Problems

1) A disk turbine with six flat blades is installed centrally in a vertical baffled tank 2 m

in diameter. The turbine is 0.67 m in diameter and is positioned 0.67 m above the

bottom of the tank. The turbine blades are 134 mm wide. The tank is filled to a

depth of 2 m with an aqueous solution of 50% NaOH at 650C, which has a viscosity

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of 12 cP and a density of 1,500 kg/m3. The turbine impeller turns at 90 rpm. What

power will be used? Given the KT = 5.8

Solution

Write down the given data and convert to SI units,

µ = 12 cP = 12 ×10–3 Pa s

n = 90/60 = 1.5 rps

2 20.67 1.5 1,500Re 84,169

0.012

an D

Since Re>104, Np = KT = 5.8

3 5 3 55.8 1.5 0.67 1,500 3,964WT aP K n D