Agitation and Mixing

Transcription

1 Agitation and Mixing Agitation: Agitation refers to the induced motion of a material in a specified way, usually in a circulatory pattern inside some sort of container. Purpose is to make homogeneous phase. Mixing: Mixing is the random distribution, into and through one another, of two or more initially separate phases. A single homogeneous material, such as tankful of cold water, can be agitated, but it can t be mixed until some other material (such as a quantity of hot water or some powdered solid) is added to it.

2 Purposes of Agitation Liquids are agitated for number of purposes which are given as follows Suspending solid particles Blending miscible liquids, e.g. Methyl alcohol and water Dispersing a gas through the liquid in the form of small bubbles. Dispersing a second liquid, immiscible with the first, to form an emulsion or suspension of fine drops. Promoting heat transfer between the liquid and a coil or jacket.

3 Agitated Vessel and Its Accessories

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5 Flow Pattern in Agitated Vessels The Flow Pattern in agitated vessels depends on the following factors; Type of Impeller Characteristics of the fluid Size and proportions of the tank Baffles Agitator The velocity of the fluid at any point in the tank has three components and overall flow pattern in the tank depends on the variations in these three components. Radial Component (It acts in a direction perpendicular to the shaft of the impeller) Longitudinal Component (It acts in a direction parallel with the shaft) Tangential / Rotational Component (It acts in a direction tangent to a circular path around the shaft)

6 Vertically Mounted Shaft Radial and Tangential components are in horizontal plane Longitudinal component is in vertical plane Radial and longitudinal are useful for mixing action Tangential component is generally disadvantageous when shaft is vertically mounted. Tangential component follows a circular path around the shaft and creates a vortex in the liquid. If the solid particles are present in the liquid, circulatory currents tends to throw the particles to the outside by centrifugal force and they move downward and to the Centre of the tank at the bottom. In an un baffled vessel circulatory flow is induced by all types of impellers i.e. axial or radial For strong swirling, flow pattern is same regardless of design of Impeller and at high speed the vortex may be so deep to reach at the impeller surface.

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8 Prevention of swirling Swirling or circulatory flow can be prevented by any of three ways a. In small tanks the impeller can be mounted off center (shaft is moved away from center then tilted in a plane perpendicular to the direction of move) b. In Large tanks, the agitator may be mounted in the side of the tank with shaft in horizontal plane but at an angle with radius. c. In large tanks with vertical agitators, swirling can be prevented by installing baffles. Four baffles are sufficient to prevent swirling and vortex formation (Even two have a strong effect on swirling effect). For turbines width of baffle need be no more than one-tweflth of vessel diameter and for propellers no more than one eighteenth of tank diameter. No baffles are required for side entering, inclined or off center propellers

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11 Impellers Impellers are divided into two major classes Axial Flow Impellers (These generates current parallel with the axis of impeller shaft) Radial Flow Impellers (These generate currents in tangential or radial directions) Following are the three main types of impellers Propellers Paddles Turbines There are also various other subtypes of impellers but the above mentioned three types solves perhaps 95% of all liquid agitated problems

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13 Propellers It is an axial flow, high speed impeller for liquids of low viscosity. Smaller propellers runs at either 1150 or 1750 rev/min and larger ones can run at 400 to 800 rev/min. The flow currents leaving the impeller continue through the liquid in a given direction until deflected by floor or wall of the vessel. The propeller blades vigorously cut or shear the liquid. A revolving propeller traces out a Helix in the fluid. One full revolution of propeller (provided no slip between liquid and Propeller) would move the liquid longitudinally a fixed distance depending on the Angle of inclination of propeller blades. The ratio of this distance to propeller diameter is known as Pitch of blade. A Propeller blade with pitch 1 is called square Pitch.

14 Pitch of impeller

15 Propellers rarely exceed 18 in. in diameter. Sometimes two propellers work in opposite directions or in push-pull to create highly turbulent zone. In deep tank, two or more may be mounted on the same shaft Propellers are used when strong vertical currents are desired e.g. when heavy solid particles are to be kept in suspension. They are not ordinarily used when viscosity of liquid is greater than 50P.

16 Paddles Agitator consists of flat paddle turning on vertical shaft They pushed the liquid radially and tangentially with almost no vertical motion at impeller unless blades are Pitched. The currents they generates travel outward to the vessel wall and then either upward or downward. In deep tanks several paddles are mounted one above the other on the same shaft. Anchors are useful for preventing deposits on a heat transfer surfaces (as in a jacketed processes) but hey are poor mixers. Industrial paddle agitators turn at speeds between 20 and 150 rev/min The total length of paddle impeller is typically 50 to 80percent of inside diameter of vessel. Width of blade is one-sixth to one-tenth its length. Slow speed paddles gives mild agitation and can work in an unbaffled tanks but at higher speeds baffles become necessary

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18 Turbines They resembles multi bladed paddle agitators with short blades, turning at high speeds on a shaft mounted centrally in the vessel. Blades may be straight or curved, pitched or vertical. Diameter of impeller turbine is smaller than with paddles, ranging from 30 to 50% of vessel diameter. The principle currents generated by turbines are radial and tangential ( the tangential component induces vortexing and swirling which must be stopped by baffles

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23 Draft tube Draft tube is a cylindrical duct slightly larger than the impeller diameter and is positioned around the impeller Used with axial impellers to direct the suction and discharge flows. The impeller draft tube system acts as a low efficiency axial flow pump The top to bottom circulation flow is of significance for flow controlled processes, suspension of solids and dispersion of gases. They are particularly useful for tall vessels having large ratio of height to diameter.

24 Standard Turbine Design S 1 = D a D t = 1 3 S 2 = E D t = 1 3 S 3 = L D a = 1 4 S 4 = W D a = 1 5 S 5 = J D t = 1 12 S 6 = H D t = 1 1

25 Power Consumption The important consideration in the design of an agitated vessel is the power required to drive the impeller. When flow is turbulent in the tank the flow can be obtained by q and E k per unit volume of fluid q can be obtained from flow number N Q = Actual Flow from impeller = Theoretical flow from impeller q nd a 3 E k per unit volume of fluid is equal to following E k = ρ(v 2 ) 2 2g c

26 Where V 2 is slightly smaller than the tip speed u 2. ratio of V 2 u 2 and the power requirement is = α. And we know V 2ʹ = απnd a P = q x E k In Dimensionless form The left hand side is the Power number N p.

27 Power Correlation Power required to rotate a given impeller, the empirical correlations of power with other variables of the system are needed. These can be represented in dimensionless form and are listed out as follows; Measurement of tank and Impeller Distance of the impeller from the tank floor The liquid depth Dimensions of the baffles Number and arrangement of the baffles Number of blades in the impeller The viscosity and density of the fluid Speed of agitator Dimensionless constant g c (because newton s law is applicable) Absence / Presence of swirling and vortex Acceleration due to gravity when the liquid is lifted up (due to agitation) from certain average height Various linear measurements can all be converted to dimensionless ratios, called shape factors, by dividing each of them by one of their number which is arbitrarily chosen as a basis. Diameter of tank, D t, or the diameter of impeller, D a, are the suitable choices for the base measurement.

28 Let the shape factors, so defined, be denoted by S 1, S 2, S 3, S n. (the diameter of the impeller, D a, is taken as base measurement. Two mixers of the same geometrical proportions throughout but of different sizes will have identical shape factors but will differ in magnitude of D a. Devices meeting these requirements are called geometrically similar. Power Number Functionality for Newtonian fluid When shape factors are temporarily ignored and liquid is Newtonian, the power of agitated vessel is a function of following variables P = f(d a, n, g c, g, μ, ρ) Application of Dimensionless analysis gives the following dimensionless groups Where N Re = nd a 2 ρ μ and N Fr = n2 D a g

29 By considering the shape factors, the power number functionality would include the following or

30 Reynolds's number Significance of Dimensionless Groups Where u 2 = Impeller tip speed = nπd a This Reynolds's number calculated from the diameter and peripheral speed of impeller. Power number It s the ratio of drag force acting on a unit area of impeller and the inertial stresses. It is analogous to a friction factor or a drag coefficient Froude Number It s the ratio of the inertial stress to the gravitational force per unit area acting on the fluid. It appears in the fluid dynamic situations where there is significant wave motion on a liquid surface. it is used to study the vortex motion during scale up of mixer. Flow number It is used to find the pumping rate of the impeller.

31 Power Correlations For specific Impellers To know the effect of geometry on the power requirement, the engineer should specify; All shape factors No. of baffles No. of impeller blades Pitch of impeller and number of blades (for propeller)

32 Curve A: Vertical blades with S 4 = 0.2 Curve B: similar impeller with narrower blades (S 4 =0.125) Curve C: For pitched blades turbine

33 Curve A: Three blade propeller centrally mounted in a baffle tank. Propellers and pitched blade turbines draw considerably less power than a turbine with vertical blades

34 Mathematical Procedure for Un-baffled tanks at low Reynolds's Number At low Reynolds number (below 300), the power curves for baffled and un-baffled tanks are identical In this region the Reynolds's number, generally avoided in practice in un-baffled tanks, a vortex forms and Froude number has an effect. Power number can be modified as follows: For given set of shape factors, the m can be related to Reynolds's number by following equation

35 Effect of System Geometry (Flat blade turbine operating at high Reynolds's number) Decreasing S 1 (impeller diameter to tank diameter) increases N p when baffles are few and narrow and decreases N p when baffles are many and wider. With four baffles and S 5 (baffle diameter to vessel diameter) set equal to 1/12, changing S 1 has almost no effect on the N p. With S 2 (height of impeller to diameter of tank) increases N p increases for disk turbine and decreases considerably for pitched blades turbine. For straight blade open turbine, the effect of changing S 4 (Impeller width to diameter of Impeller) depends on number of blades. For six blade S 4 is directly proportional to N p but for four blade turbine N p increases S

36 With pitched blade turbine the effect of blade width on power consumption is much smaller than with straight blade turbines. Two straight blade turbines on the same shaft draw about 1.9times as much power as one turbine alone, provided the spacing the two impellers is at least equal to the impeller diameter. Two closely spaced turbines may draw as much as 2.4times as much power as a single turbine. The shape of the tank has little effect on the Np. The power consumed by horizontal cylindrical vessels is same as in a vertical vessel for both baffled or unbaffled.