MO module 7 of mechanical operations course

MO module 7 of mechanical operations course

1. Module 7 Agitation Principles of Agitation: Agitation vessel Impellers - Flow Pattern in Agitated Vessel - Power Consumption in Agitated vessel- Calculation of power consumption in agitation vessel.

2. Definitions Agitation- refers to an induced motion of a material in a specified way usually in a circulatory pattern inside some sort of container. Mixing- is the random distribution of two or more initially separate phases .

3. Purpose of Agitation Blending of two miscible liquids Dissolving solids in liquids Dispersing gas in liquid as fine bubbles Suspending fine solid particles in a liquid Agitation of fluid to promote HT between the fluid and a coil or jacket.

4. Construction and Flow patterns of Impellers There are two types of impellers. Axial flow impellers Radial flow impellers Axial flow impellers make an an angle of less than 90 degrees with the shaft. They generate flow currents parallel to axis of the shaft. Radial flow impellers have blades parallel to the axis of the shaft. They generate flow currents in tangential or radial directions. Impellers are further classified into three sub types: Propellers Paddles Turbines Propellers and turbines are axial flow impellers, whereas paddles, flat blade, curved blade, disc blade turbines are radial flow impellers

5. Propeller Most popularly used for agitating liquids of low viscosity Effective for very large vessels One full revolution would move the liquid longitudinally a fixed distance depending on the angle of inclination Distance moved/propeller dia = pitch Speed 400 – 1750 rpm 3 bladed marine propeller with square pitch commonly employed in process industry Off center, inclined or side entering propeller used for special purposes.

6. Paddle Large, slow speed impellers usually with 2 or 4 blades Push the liquid radially and tangentially. Tangential motion cause vortex formation and swirling stopped by using baffles and diffuser ring. Speed 20 – 150 rpm Length = 60 – 80% tank dia. Width = 10 – 15 % of length

7. Concept of swirling and Vortex If a low viscosity liquid is stirred in an unbaffled tank by a centrally mounted agitator, there is a tendency for a swirling flow pattern to develop, for the lighter fluid usually air is to be drawn in to form vortex at the surface of liquid. Vortex is produced due to centrifugal force acting on the rotating liquid.

8. Prevention of swirling and vortex formation There are three methods for the prevention of swirling and vortex formation Off centre mounting of the impeller Use of baffles Use of diffuser rings with turbines In case of presence of baffles, the vertical flow currents are increased and there is more rapid mixing of the fluid. The addition of baffles in a vessel considerably increases the power requirement for mixing.

9. Power consumption of Impellers Usually electrical power is used to drive impellers in agitated vessels An empirical correlation of power with other variables of a system allows us to do fairly accurate prediction of power requirement of a given impeller to rotate at a given speed. Such correlations cab be obtained by using a method of dimensional analysis. P/(N 3 D a 5 ρ) = F((ND a 2 ρ/µ)(N 2 D a /ρ )) N p = f( N Re , N Fr ) The Froude number represents the influence of gravitation and affects the power consumption only when vortex is present. For Reynolds number below 300, vortex may not be observed even for unbaffled vessel

10. N p = f( N Re ) The power consumption is related to the density, viscosity of liquid, rotational speed and impeller diameter by plotting power as a function of Reynolds number

11. At low Reynolds number: When Reynolds number greater than 10000: Unit of g c = kg.m /N.S 2

12. Problem For geometrically similar baffled stirred tanks, the power number is known to remain constant at high Reynolds number. (a) Let P be the power supplied per unit volume of the fluid, N the revolutions per second of the agitator, ρ the density of fluid, the viscosity of the fluid and D the diameter of impeller. Then determine a, b, c and d in the following equation: (b) What is the effect of Froude number on P  

13. A six blade turbine agitator of diameter 60 cm is installed centrally in tank with flat bottom of diameter 180 cm, at a height of 60 cm from the bottom. The tank is filled with a solution of viscosity 10 Cp and of 1.45 g/ml density. The speed of agitation is 90 rpm. The tank is baffled. Calculate the power required in HP. Power number = 1.05 for Reynolds number greater than 300

14. N Re K 10,000 5.8 60,000 6.0 80,000 7.0 A flat blade turbine with six blades is installed centrally in a vertical tank. The tank is 1.83 m in diameter; the turbine is 0.61 m in diameter and is positioned 0.61 m from the bottom of the tank. The tank is filled to a depth of 1.83 m with a solution of 50% caustic soda which has a viscosity of 12 cp and a density of 1.5 gm/cc. The turbine is operated at 90 rpm. The tank is fitted with four baffles, each having a width of 19 cm. What will be the power consumption for the operation of the baffled mixer?

15. D a = Impeller diameter = 61 cm μ = Viscosity = 12 cp = 0.12 poise ρ = 1.5 g/cc N = Revolution per second = speed in RPM/60 = 90/60 = 1.5 rev. per second Reynolds No. N R e = (ND a 2 ρ )/ μ = {1.5 x (61) 2 x 1.5}/0.12 = 69768 So flow is turbulent For turbulent flow: Np = power number = C = constant = 6.0 And power is given by

16. Problem An agitated baffle vessel is being used to prepare a uniform solution of viscosity 2 cP , running the agitator at 100 rpm, so as to obtain a Reynolds number of 50000. If the contents of the vessel are replaced by a solution of viscosity 4 cP , and the agitator rpm is increased to 200 rpm, by how much will the power requirement change?

17. For geometrically similar baffled stirred tanks, the power number is constant at high Reynold’s number. (a) Let P be the power supplied per unit volume of fluid. N be the revolutions per second of the agitator, ρ be the density of fluid, µ be the viscosity of fluid and D be the diameter of impeller. Then determine a, b, c and d in the following equation: (b) What is the effect of Froude Number on P?  

18. Mixers for cohesive solids (pastes) 1. ( i ) Pony mixer (ii) Beater mixer 2. Kneaders, Dispersers, Masticators 3.Bnanbury mixer 4. Continuous kneaders 5. Mixer Extruders 6. Mixing Rolls 7.Muller Mixer 8. Pug Mill

19. Mixers for cohesive solids Ribbon blenders Internal screw mixer Tumbling mixers Impact wheels

20. Problem on Mixing A biscuit is prepared by mixing flour and other ingredients along with tracer material (2% mass). After 10 minutes of mixing 6 random samples are collected and their composition (%) is given below After 10 min 2.021 1.925 1.826 2.125 2.210 2.015 Calculate Mixing index after 10 min of mixing

21. Problem A six blade turbine agitator of diameter 60 cm is installed centrally in tank with flat bottom of diameter 180 cm, at a height of 60 cm from the bottom. The tank is filled with a solution of viscosity 10 C p and density of 1.45 g/ml. The speed of the agitation is 90 rpm. The tank is baffled. Calculate the power required.

22. Solution N Re = 87000 N p = constant = 1.05 (given) P = 400 kg.m 2 /s 3 P = 400 W