CHE 482 – EQUIPMENT DESIGN
AGITATED AND STIRRED VESSELS Engr. Ronnie V. Flores
2nd Semester AY 2009-2010
TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES ‐ MANILA DEPARTMENT OF CHEMICAL ENGINEERING
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AGITATED AND STIRRED VESSELS
REQUIREMENTS FOR THE DESIGN OF AGITATED VESSELS: 1. Impeller Design a. Type of Impeller b. Impeller Diameter c.
Position of impellers
2. Power requirement to drive the agitation 3. Stirrer Speed 4. Baffle design (if needed) 5. Mixing Time SELECTION OF TYPE OF IMPELLER Use figure 10.57 Coulson and Richardson’s Chemical Engineering Volume 3, 4th edition – a function of tank diameter and liquid’s viscosity IMPELLER SIZE For standard turbine design (source: Unit Operations for ChE by McCabe, 7th edition)
1 3 1 1 12
1 5 1 4
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From Chemical Process Equipment Selection and Design by Stanley Walas,
THE VESSEL ; A dished bottom requires less power than a flat one. ; When a single impeller is to be used, a liquid level equal to the diameter is optimum, with the impeller located at the center for an all-liquid system. Economic and manufacturing considerations, however, often dictate higher ratio of depth to diameter. BAFFLES ; Except at very high Reynolds numbers, baffles are needed to prevent vortexing and rotation of the liquid mass as a whole. ; A baffle width one-twelfth the tank diameter, w = 4/12; a length extending from one half the impeller diameter, d/2, from the tangent line at the bottom to the liquid level, but sometimes terminated just above the level of the eye of the uppermost impeller. ; When solids are present or when a heat transfer jacket is used, the baffles are offset from the wall a distance equal to one sixth the baffle width. ; Four radial baffles at equal spacing are standard; six are only slightly more effective, and three appreciably less so. ; When the mixer shaft is located off center (one-fourth to one-half the tank radius), the resulting flow pattern has less swirl, and baffles may not be needed, particularly at low viscosities.
ChE 482 – Equipment Design
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DRAFT TUBES ; A draft tube is a cylindrical housing around and slightly larger in diameter than the impeller. ; Its height may be little more than the diameter of the impeller or it may extend the full depth of the liquid, depending on the flow pattern that is required. ; Usually draft tubes are used with axial impellers to direct suction and discharge streams. ; An impeller-draft tube system behaves as an axial flow pump of somewhat low efficiency. Its top to bottom circulation behavior is of particular value in deep tanks for suspension of solids and for dispersion of gases. IMPELLER LOCATION Source: Chemical Process Equipment Selection and Design by Stanley Walas Impeller clearance
Maximum level,
Number of
H/Dt
impellers
Lower
<25,000
1.4
1
H/3
<25,000
2.1
2
Dt/3
<25,000
0.8
1
H/3
<25,000
1.6
2
Dt/3
Viscosity, cP
Upper (2/3)H (2/3)H
; Another rule is that a second impeller is needed when the liquid must travel more than 4 ft before deflection. ; Side entering propellors are placed 18-24 in. above a flat tank floor with the shaft horizontal and at a 10” horizontal angle with the centerline of the tank; such mixers are used only for viscosities below 500 CP or so. ; In dispersing gases, the gas should be fed directly below the impeller or at the periphery of the impeller. Such arrangements also are desirable for mixing liquids. POWER REQUIRED TO ROTATE AN AGITATOR IMPELLER 1. Determine the turbulent power number, NP, for impeller geometry. •
Figure 9.13 (Unit Operations for ChE by McCabe, 7th edition) – Power Number versus Reynolds number for turbines and high efficiency impellers
•
Figure 9.14 (Unit Operations for ChE by McCabe, 7th edition) – Power Number versus Reynolds number for marine propellers and helical ribbons
•
Figure 9.15 (Unit Operations for ChE by McCabe, 7th edition) – for pseudo-plastics fluids
•
For non-newtonian fluids, Re can be calculated using equation 9.23 (Unit Operations for ChE by McCabe 7th edition)
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Where: - apparent viscosity of non-newtonian fluid - flow consistency index of non-newtonian fluid - average shear rate
2. Compute the shaft horsepower required to rotate the impeller
Where: - Power number - rotational speed, revolution per unit time - Power requirement, kW or ft-lbf/s - impeller diameter - density of the liquid
o
for Re less than 10, use equation 9.20 (Unit Operations for ChE by McCabe 7th edition)
Where: - taken from table 9.2 (Unit Operations for ChE by McCable, 7th edition) - viscosity of the liquid
o
for Re more than 10,000, use equation 9.22 (Unit Operations for ChE by McCabe 7th edition)
Where: - taken from table 9.2 (Unit Operations for ChE by McCable, 7th edition) 3. Select a standard motor horsepower •
Assume 85% efficiency due to losses through the gear reducer, slight deviations in actual speed and fluctuations in process conditions
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DESIGNING AN AGITATOR TO BLEND TWO LIQUIDS 1. Determine the required agitation intensity •
One measure of the amount of liquid motion in an agitated tank is velocity. However, by the very nature of mixing requirements, liquid velocities must be somewhat random in both direction and magnitude.
•
Since actual velocity is difficult to measure and depends on location in the tank, an artificial, defined velocity called “bulk velocity” has been found to be a more practical measure of agitation intensity. “Bulk velocity” is defined as the impeller pumping capacity (volumetric flow rate) divided by the cross-sectional area of the tank.
•
The magnitude of bulk velocity can be used as a measure of agitation intensity for most problems involving liquid blending. Bulk velocities in the range from 0.1 to 1.0 ft/s (0.03 to 0.3 m/s) are typical of those found in agitated tanks. An agitator that produces a bulk velocity of 0.1 ft/s is normally the smallest agitator that will move liquid throughout the tank. An agitator capable of producing a bulk velocity of 1.0 ft/s is the largest practical size for most applications.
•
Reference: Table 12.1 (Handbook of Chemical Engineering Calculations by Nicolas Chopey, 3rd edition)
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2. Compute for the required impeller pumping capacity
Where: - impeller pumping capacity - equivalent tank diameter - bulk velocity (table 12) 3. Select impeller diameter and determine required agitator speed a. Select an impeller diameter b. Compute initial estimate of impeller Reynolds number; assume initial agitator speed c.
Determine pumping number, Nq, and compute speed i. Use figure 12.3 to get Nq
ii. Compute for agitator speed
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Where: - flow number d. Recalculate if n computed is not the same with the assumed n 4. Select standard speed and motor horsepower 5. Specify the number and location of impellers TIME REQUIRED FOR UNIFORM BLENDING 1. Compute for the Reynolds number 2. Determine blending time factor ntT (Figure 9.17 – Unit Operations for ChE, 7th edition) 3. Compute for blending time using equation 9.16 (Unit Operations for ChE, 7th edition)
o
Fig 9.17 (Unit Operations for ChE, 7th edition) – Correlation of blending times for miscible liquids in a turbine-agitated baffled vessel; Re plotted vs blending time factor, fT (Equation 9.31)
Where: - blending time factor (from fig 9.16) - blending time - rotational speed, revolution per unit time - blending time factor (from fig 9.17) AGITATED SOLID SUSPENSION 1. critical stirrer speed (Equation 9.35, Unit Operations for ChE by McCabe, 7th edition) ∆ . . . . . Where: - critical stirrer speed - shape factor (Table 9.4, Unit Operations for ChE by McCabe, 7th edition) - kinematic viscosity - average particle size
∆
- density difference - density of liquid - 100 x weight of solid/weight of liquid
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2. Power Consumption – Fig 9.20 (Unit Operations for ChE by McCabe, 7th edition); tank diameter plotted vs power per unit volume; use the Buurman curve with sand as reference SHAFT DESIGN FOR TURBINE AGITATOR 1. Determine the hydraulic loads (torque and moment) on the shaft – to rotate the agitator, the shaft must transmit torque from the drive to the impellers.
. Where: - maximum torque - bending moment on the shaft - motor power (divided by the number of impellers) - agitator speed - distance of impeller from the agitator drive 2. Determine the minimum shaft diameter for strength
Where: - shaft diameter due to shear stress - shaft diameter due to tensile stress - allowable shear stress - allowable tensile stress CHOOSE THE LARGER SHAFT DIAMETER 3. Calculate the natural frequency of the agitator shaft
.
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Where: - critical speed - shaft diameter - Modulus of Elasticity - shaft extension (length) - spacing of bearings that support the shaft - density of material - equivalent weight of impellers and shaft at shaft extension For two impeller system,
= Where: - Weight of the lower impeller - Weight of the upper impeller - distance of the upper impeller from the drive - unit weight of the shaft NOTE: DESIGN SPEED < 65% OF CRITICAL SPEED RULES OF THUMB FOR AGITATOR AND MIXERS 1. Mild agitation is obtained by circulating the liquid with an impeller a: superficial velocities of 0.1-0.2 ft/sec, and intense agitation at 0.7-1.0 ft/sec. 2. Intensities of agitation with impellers in baffled tanks are measured by power input, HP/1000 gal, and impeller tip speeds: Operation
HP/1000 gal
Blending
0.2 – 0.5
Homogenous reaction
0.5 – 1.5
7.5 – 10.0
Liquid-liquid mixtures
5.0
15 – 20
5.0 – 10.0
15 – 20
Liquid-gas mixtures Slurries
Tip speed (ft/min)
10.0
3. Proportions of a stirred tank relative to the diameter D: liquid level = D; turbine impeller diameter D/3; impeller level above bottom = W/3; impeller blade width = D/l5; four vertical baffles width = D/10. 4. Propellers are made a maximum of 18 in., turbine impellers to 9 ft. 5. Gas bubbles sparged at the bottom of the vessel will result in mild agitation at a superficial gas velocity of 1ft/min, severe agitation at 4 ft/min.
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6. Suspension of solids with a settling velocity of 0.03ft/sec is accomplished with either turbine or propeller impellers, but when the settling velocity is above 0.15 ft/sec intense agitation with a propeller is needed. 7. Power to drive a mixture of a gas and a liquid can be 25 – 50% less than the power to drive the liquid alone. 8. In-line blenders are adequate when a second or two contact time is sufficient, with power inputs of 0.1-0.2HP/gal.
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from Coulson and Richardson’s Chemical Engineering Volume 3, 4th edition
ChE 482 – Equipment Design
