Agitation

AGITATION

Introduction to Principles and Practice

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Course Contents

• Agitation• Flow patterns• Types of Impellers• Power Calculation• Mixing• Degree of Mixing• Scale-up of Agitator Design

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Agitation-refers to the induced motion of a material in a specified way, usually in a circulatory pattern inside some sort of container.

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Examples of Processes that uses Agitation

• Blending of two miscible liquids• Dissolving solids in liquids• Dispersing a gas in a liquid as fine bubbles,

such as oxygen in a suspension of microorganisms for waste-treatment

• Suspension of fine solid particle, such as metallic pigments in paint

• Agitation of a fluid to eliminate temperature gradients

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Agitation Equipment

• Cylindrical vessel with a vertical axis• Vessel bottom is rounded• Liquid depth is approximately equal to

the diameter of the tank• An impeller is mounted on an overhung

shaft. Shaft is driven by a motor• The impeller creates a flow pattern in

the system, causing the liquid to circulate through the vessel and return eventually to the impeller

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Impellers

• Divided into two classes: – Axial-flow impellers

generate currents parallel with the axis of impeller

– Radial-flow impellersgenerate currents in a tangential or radial direction.

• Three main types of impellers:– Propellers– Paddles– Turbines

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Propellers

• Axial flow high speed impeller, for liquids of low viscosity

• Small impellers turn at full motor speed• Pitch of propeller: a propeller with a

pitch of 1.0 is said to have square pitch• Rarely exceed 18” in diameter

regardless of the size of the vessel• In a deep tank two or more propellers

may be mounted on the same shaft

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Propellers

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Paddles

• Flat paddle turning on a vertical shaft• Two-bladed and four-bladed paddles

are common• Sometimes the blades are pitched;

more often they are vertical• Push the liquid radially and tangentially

with almost no vertical motion• In deep tanks several paddles are

mounted one above the other on the same shaft

-contd..

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Paddles

• In some designs blades conform to the shape of the vessel so that they scrape the surface or pass over with close clearance– Eg. Anchor agitators

• Anchor agitators are useful for preventing deposits on a heat transfer surface

• Industrial paddle agitators turn at speed between 20 and 150 rpm

• Total length of impeller is 50-80% of the ID of vessel

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Paddles

Four bladed

Anchor type

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Turbines

• Multi-bladed paddle agitators with short blades, turning at high speeds

• Blades may be straight, or curved, pitched or vertical

• Impellers may be open, semi-enclosed, or shrouded

• Dia of impeller is smaller than with paddles, ranging from 30 to 50% of vessel dia

• Effective over a wide range of viscosities

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Turbines

Open straight-bladeturbine Open curved blade

turbine

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Selection of Impellers

• In the direction of viscosity increasePropeller Turbine Paddle Anchor Helical ribbon Helical screw

Speed of impeller decreases in the above order.

• Propellers: up to 10,000 cP;Turbines: up to 15,000 cP;Anchors: upto 100,000 cP

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Flow patterns

• Depends on the type of impeller, characteristics of the fluid, size and proportions of tank, baffles and agitator

• Velocity of fluid has three components, and the overall flow pattern in the tank depends on the variations in these velocity components from point to point

• Three velocity components: – Radial, longitudinal, and rotational or

tangential

-contd..

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Flow patterns

• Radial component acts in a direction perpendicular to the shaft of the impeller

• Longitudinal component acts in a direction parallel with the shaft

• Tangential or rotational component acts in a direction tangent to a circular path around the shaft

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

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Vortex formation

• When the shaft is vertical and centrally located in the tank, the tangential component is generally disadvantageous

• The tangential flow follows a circular path around the shaft, and creates a vortex at the surface of the liquid

• 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

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Vortex formation and Swirling

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Prevention of Swirling

• Off-centered mounting of impeller • Mounting agitator with inclination

to the vertical axis• Installing baffles

– Baffles are not generally required with high viscosity liquids where vortexing is not a problem

• Using draft tubes

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Agitator Flow patterns

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Degree of Agitation

• Agitator tip-speed is commonly used as a measure of degree of agitation

• Tip-speed = D n• Expressed in

feet/min (fpm)

Low 500-650 fpm

Medium

650-800 fpm

High 800-1100 fpm

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Std Speed of Impellers

• Motor speed: 1420-1450 rpm for 50Hz, AC

• Worm gear reducers with ratio: 5:1 to 60:1

Impeller speed, rpm

Gear ratio

284 5:1

190 7.5:1

142 10:1

100 15:1

71 20:1

57 25:1

48 30:1

37 40:1

30 50:1

25 60:1

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Power consumption

• Power required to rotate a given impeller depends on:– important measurements of tank and

impeller– viscosity and the density of the

liquid– speed of agitator– acceleration of gravity g

• Empirical correlations of power with the above variables by dimensional analysis are available.

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Power correlation

• Power P is a function of the variables:

• By dimensional analysis:

• Taking account of shape factors:

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Dimensionless Groups

• Power number

• Reynolds number

• Froude number

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Power Correlations

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Calculation of power consumption

• From the definition of NP

• At low Reynolds number

• At high Reynolds number

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Mixing

• Mixing refers to the random distribution, into and through one another, of two or more initially separate phases

• A single homogenous material, such as a tank full of cold water can be agitated, but it can not be mixed until some other material is added to it

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Factors enhancing mixing

• Low interfacial tension that inhibits the formation of interfaces

• Similar densities that prevent separation by stratification induced by gravity and centrifugal fields

• Low viscosities that promote fluidity and the penetration of one fluid element into another.

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Uniformity of Mixing - Measuring

By Various kinds of tracer techniques:• A dye is introduced and the time for

attainment of uniform color is noted• A concentrated salt solution is added as tracer

and the measured electrical conductivity tells when the composition is uniform

• The residence time distribution is measured by monitoring the outlet concentration of an inert tracer. The shape of response curve is compared with that of a ideally mixed tank

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Degree of Mixing - Quantification

• Standard Deviation:

wherexm (with an over-bar) is the mean fractional

concentration

xi = the fractional concentration of the component in the i-th sample

N = the number of samples taken

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Mixing Index

where

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How long to Mix

• Mixing index decrease with time according to

where k is the mixing rate constant; and tm is the mixing time

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Scale-up of Agitator Design

• When a small unit is built before the larger or production unit – pilot plant

• When a small unit is built after the production unit - model

• Scale-up requires three types of similarity between pilot-plot unit and full-scale unit:– Geometric similarity– Kinematic similarity– Dynamic similarity

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Geometric similarity

• Refers to linear dimensions• Two vessels of different sizes are

geometrically similar if the ratios of the corresponding dimensions on the two scales are the same

• If photographs of two vessels are completely super-impossible, they are geometrically similar

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Kinematic Similarity

• refers to motion

• requires geometric similarity and the same ratio of velocities for the corresponding positions in the vessels

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Dynamic Similarity

• concerns forces

• requires all force ratios for corresponding positions to be equal in kinematically similar vessels

• the significant dimensionless parameters must be equal for model and prototype

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Example of Scale-up

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Necessary conditions for Effective Scale-up

• First the regime must be a relatively pure one. Dynamic similarity should depend chiefly upon a single dimensionless group that represents the ratio of applied to the opposing forces

• Second, the regime should not change as vessel size goes from small to the larger scale.

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References

• McCabe & Smith, Unit Operations of Chemical Engineering, McGraw Hill

• Treybal, Mass Transfer Operations, McGraw Hill

• Perry, Chemical Engineers Handbook, McGraw Hill

• http://www.erpt.org/014Q/youa-00.htm • http://www.ces.clemson.edu/

chemeng/undergraduate/uolab/theoryof.htm

Thank You