Design Calculations For Slurry Agitators 6p3o5f

Design Calculations for Slurry Agitators RAJENDRA KUNWAR FollowRAJENDRA KUNWAR

Associate Vice President - Projects at JSW Steel Limited

Hi Friends, Today I am presenting the gist of my technical paper on "Motor rating calculations for slurry mixing agitators in Alumina refinery" which has been published recently in aluminum issue of the magazine "Minerals & Metals Review" (page 30 and 31 in MMR, August 2011 issue). In various technical forums, process experts as well as equipment manufacturers have opined that the design of agitators for mixing bauxite, residue and hydrate in Alumina refinery is complicated and tricky issue. In this paper, we will discuss the subject with brief description of involved terminology, associated design parameters and methodology with sample motor rating calculations for the slurry mixing agitator of a Pre-desilication tank of Alumina refinery.

Method to arrive at motor rating: Impeller power for slurry mixing agitator is calculated using following mathematical relationsImpeller Power, P = Ni * ρ *N3 * Di5/(16*104) h.p.

Where Di = Diameter of impeller in meters, N = Revolution per minute for impeller, Ni = Power number for impeller and ρ = Specific gravity of slurry.

Sample calculations: Simplified calculations to arrive at the motor rating for the agitator of Pre-desilication tank of around 3000 m3 gross capacity with realistic assumptions have been presented belowFluid Height in Tank, H = 16 m and Diameter of tank, D = 14 m Slurry volume in tank = π *D2*H/4 = π * (14)2*16 /4 = 2463 m3 Solid consistency in Slurry = 50 % (w/w), Specific gravity of slurry, ρ = 1.602, Viscosity of slurry, μ = 550 Agitator Impeller Diameter, D= 33 % of tank diameter = 14 * 33% m = 4.62 m Tip speed of Impeller = 290 m/minute, rpm.

Drive motor RPM = 1500

Gear Box Reduction Ratio = 75 ∴ Agitator RPM, N = Drive Motor RPM/Gear Box Reduction Ratio = 1500/75 = 20 rpm

Flow Number Nf = 0.56 and Power Number, figures)

Np = 0.51 (assumed

∴ Pumping Capacity = Nf. Np.D3 m3/minute = 0.56 * 20 * (4.62)3 = 1104.44 m3/min. = 18.41 m3/sec. Area of Tank

= π D2 = π (14)2 / 4 = 153.94 m2

Bulk fluid Velocity

= pumping capacity/area of tank

= 1104.44 / 153.94= 7.18 m/min.= 23.55 ft./min. Degree of Agitation = bulk fluid velocity / 6 (For 6 ft/min., degree of agitation =1 and Degree of agitation varies from 0 to 10) = 23.55 / 6 = 3.93 ~ 4 Annular Area = π * (Dt2- Di2 ) /4 Where Dt = Diameter of tank meters.

and

Di= Diameter of impeller in

= 3.14 * (142 – 4.622) / 4 = 137.18 m2 Rising velocity of particles = pumping capacity / annular area = 1104.44 / 137.18 = 8.051 m/min. = 0.1342 m/sec. Tank Turnover rate = Pumping capacity / tank capacity = 1104.44 / 2463 = 0.45 times / min.

Impeller Power Number Ni Shaft Power,

P

= 0.51

= Ni* ρ *(D)5 * N3 /(16 *104)

Where Ni = Impeller power no., D = Diameter of impeller in meters, Shaft RPM, N = revolutions per minute ∴ Shaft Power, P = 0.51*1.602* (4.402)5*203/ (16 *104) = 85.98 h.p. Taking Gear Box Efficiency = 80% and Drive Motor Efficiency = 95%, Design margin = 1.15 ∴ Drive Motor Rating = 1.15 * 85.98/(0.80 * 0.95) =130 h.p. = 97.0 kW.

Thus the drive motor of about 100 kW shall be adequate for successful operation of agitator of 3000 m3 capacity Pre-desilication tank in Alumina refinery.

Mixing 101: Flow Patterns & Impellers MIXING FLOW PATTERNS & IMPELLER TYPES In our article on 4 Impeller Types and Their Applications, we provided an overview on the most common types of impellers used in industrial mixing. Now we’ll go into more detail about each impeller type and their influences on the mixing process. Our focus on impellers is due to the fact that they are the part of the mixer that does the actual mixing: as they rotate they create fluid flow. These flow patterns are the primary considerations when deg a mixer because creating the right flow pattern is critical to achieving the desired result. The most common flow patterns in mixing are axial (down and up) and radial (side to side) flow. These flow patterns also describe the generic classes of impellers: axial and radial.

1. Axial Flow Impellers Axial (down and up) pumping is an important flow pattern because it addresses two of the most common challenges in mixing; solid suspension and stratification. In this process both the superficial and annular velocities can be calculated to

determine and control the level of mixing. (If your axial impeller is causing swirling or vortexing, check out our previous Mixing 101 posting Baffled by Baffles?) Here are some of the most common axial impellers: A. Marine-type Propellers Viscosity: 0 – 5,000 s Commonly used on marine boats, the propellers are often used in small portable direct drive mixer applications because they’re economical and efficient. However, in larger applications they’re seldom used because of their price and weight.

B. Pitch Viscosity: 0 – 50,000 s The pitch blade impeller is the most versatile impeller and was the standard until the development of the airfoil. They’re useful in blending two or more liquids and are effective in low bottom clearance with less liquid submergence.

C. DynaflowTM (Hydrofoils) Viscosity: 0 – 3,000 s This impeller uses the Bernoulli’s principle in the design of its blade. The camber of the blade increases the efficiency of the impeller, reducing its power / pumping ratio. A more technical benefit is the laminar flow created by the camber of this impeller. This camber reduces turbulence (shear) substantially. That is why it is selected for shear-sensitive applications as well.

2. Radial Flow Impellers Unlike axial impellers, radial impellers are commonly selected for low level mixing (known as a tickler blade) or elongated tanks. They typically give high shear rates because of their angle of attack. They also have a relatively low pumping number, making them the most sensitive to viscosity. Radial impellers do not have a high tank turnover flow like axial flow impellers.

Impeller Selection As you can see, the first step to meeting your mixing objective is to identify your desired flow pattern, which is dictated by the impeller. Next, you must consider the 4 main factors for configuring your mixer. From there, you must address the mechanical requirements of your mixing process: pumping or flow. The mechanical requirements to produce flow or torque per unit volume, the most important relationship in mixing, are explained next.

Mixing Glossary Shear Stress 

Parallel-acting force where 2 layers inside the fluid slide against each other. This is in contrast to compression (perpendicular-acting force), tension (stretching force), and torsion (twisting force).

Viscosity 

Internal fluid resistance thought of as the “thickness” or “resistance to flow” of the liquid (i.e. water has viscosity of 1 centipoise vs hand cleaner, which is around 3,000 centipoise).

Power Number (NP) 

Constant used to calculate power draw, unique to each type of mixing impeller.

Pumping Number (NQ) 

Constant used to calculate flow or pumping rate, derived empirically for each unique shape of impeller.

Superficial Velocity 

Velocity of the fluid being pumped downward by the impeller.

Annular Velocity 

Rate at which the liquid is traveling upwards inside a tank past the impeller.

Solid Suspension 

State of a solid when its particles are mixed with, but don’t dissolve in the fluid and are capable of separation (i.e. sand in water).

Stratification 

Separation of 2 immiscible liquids due to density variation. Such circumstances occur naturally: for example, due to variations in temperature in the atmosphere or temperature and salinity variations in the ocean.

Mixing 101: Optimal Tank Design UNDERSTANDING HOW TANK DESIGN AFFECTS MIXING Apart from the actual mixer, the design of the mixing tank is the single most important factor in producing a successful result in any process. In order to allow optimal performance from a mixer’s impeller, it is essential to create an environment that s both correct impeller positioning and appropriate liquid coverage of the impeller. Incorrect positioning negatively affects the performance of a mixer, the quality of a product, and may even be detrimental to the performance life of the mixer drive. When looking at tank designs, vertical cylindrical, and square or rectangular tanks are most common. In the process of selecting the optimal tank design for an application there are certain rules of thumb to observe.

1. Liquid Level to Tank Diameter Ratio For most mixing applications the ideal liquid level to tank diameter ratio is 0.8, however, any ratio that is close to 1-to-1 is sufficient. A ratio that is too small does not allow proper axial mixing in the tank. Anything less than a 0.6 ratio should be avoided. When the ratio is in excess of 1.4, dual impellers should be employed. Any time that the liquid level to tank diameter ratio exceeds 2.0 the tank selection should be re-evaluated, as these slim tanks are not the most cost-effective solutions for mixing. As the mixer shaft length extends, so does the price of the mixer. For example, if we take a typical 5,000-gallon tank based on the ideal scenario and the slim tank scenario, the following will occur:

Tank Dimensions

Liquid Level

Volume

Liq. Level to Dia. Ratio

Typical Mixer Budget Price

10′ Dia x 10′ H

8′ H

5,000 Gallons

0.8

$6,500

7.5′ Dia x 16′ H

15′ H

5,000 Gallons

2

$12,000

As you can see from the table above the typical mixer price almost doubles. Vertical Cylindrical Tanks

Vertical cylindrical tanks are the most common type of tank in use. A key consideration for cylindrical tanks is to ensure that they are either baffled or offset-mounted to prevent swirling from occurring. Refer to section 2 below (“The Use of Baffling”) for details. Generally baffles are not required for smaller tanks (<5,000 gallons in volume or <10’ height). However, for larger tanks, it is much more cost effective to install baffles than to invest in a more expensive, more heavy-duty mixer that is offset-mounted. Rectangular Tanks

Rectangular tanks have an equivalent diameter that can be calculated by taking the square root of Length x Width and multiplying it by 1.13. A similar liquid level to equivalent tank diameter ratio of 0.8 applies. Rectangular tanks can be effective when used for blending, as these tanks are selfbaffling. However, rectangular tanks are not recommended for solid suspension because packets of solids will form in the corners. These “dead spots” will occur in a tank with corners. Therefore, a greater level of mixing is required than is needed in a cylindrical tank of equal size to achieve a similar result. Cone or Round Bottom Tanks

Some tanks will have a round (dish) or cone bottom. Below are some standard guidelines about approaching mixing for these tanks. 1. Cone bottom: Ideally the cone angle should be less than 15°, but anything less than a 30° angle is acceptable. If a cone is too deep, it just becomes that much more difficult to provide good mixing inside it. 2. Round Bottom: The same rules apply for a round bottom as for a cone. Generally a round bottom is better for solids suspension as there are no sharp angles in the tank, so it eliminates dead spots. 3. Baffles: If a cone/round bottom tank is very deep, baffles can be put inside this part of the tank as well, to promote good axial mixing and prevent swirling from occurring.

2. The Use of Baffling Rectangular tanks are self-baffling, so the use of baffles is a requirement when using cylindrical tanks only. If an agitator is center-mounted in an un-baffled cylindrical tank, it produces a swirling motion, which is very inefficient. As an example, imagine two particles swirling in a circular motion, they will always be chasing each other and will not mix. There are two solutions to consider: 1. Install Baffles: Installing baffles in the tank is the best option. 2. Offset the Mixer: Mounting the mixer with an offset of approximately 1/6th of the tank diameter will prevent swirling from occurring. The drawback to this option is that the unbalanced forces will create greater stress on the mixer shaft and will require a larger heavy-duty mixer. This becomes cost-prohibitive for larger applications with shaft length requirements over 10’. Typical Baffle Arrangements

Baffles are typically mounted 1/72 of the tank diameter off the wall of the tank, and are 1/12 of the tank diameter in width. The optimal installment is comprised of four baffles within a tank, but the use of three baffles is sufficient for most applications. Baffles should fully extend the length of the tank, leaving some space at the bottom to avoid the build-up of solids. Therefore, the configuration for a 12’ diameter tank would be 1’ wide baffles mounted 2” off the tank wall.

Mixing 101: Baffled by Baffles? HOW BAFFLE CONFIGURATION CAN OPTIMIZE INDUSTRIAL MIXING In our previous posting on configuring your mixer, we learned that the tank type and volume, viscosity, specific gravity and the process are key factors the mixing process. In this article, we dive into how baffle configuration and mixer mounting can prevent the undesirable flow pattern of swirling. Let’s look at a common tank configuration: an un-baffled cylindrical tank. If a mixer is center-mounted in this tank, what we see is a very inefficient flow pattern: the tangential velocities coming from the impeller cause the entire fluid mass to spin (Fig. 1). Basically, the entire fluid (and its solids) moves like a merry-go-round. In solid suspension applications, the solid particles will swirl around at the bottom of the tank: no axial (top to bottom) flow is created to lift them up and suspend them in the fluid.

FIGURE 1. Center-mounted mixer in an unbaffled cylindrical tank

There are three ways swirling can be prevented, and we’ve listed them by preference: 1. Installing baffles in tanks 2. Offset angle mounting of mixers 3. Offset vertical mounting of mixers Using baffles or offset mounting techniques will generate unbalanced loads that will act on the mixer shaft. When these unbalanced loads become significant, a heavierduty agitator gearbox and bearing are needed. As a result, the mixer is more expensive. Baffles are our first choice because the loads generated are much less than those generated by offset angle or vertical mounting techniques. For smaller tanks (<10′ diameter), offset mounting will work just fine, and the extra cost associated with compensating for unbalanced load is minimal. For larger tanks, however, it becomes expensive to go with the heavier-duty mixer, and installing baffles is more cost effective.

Baffle Design Baffles are long, flat plates that attach to the side of the tank to prevent swirling & promote top to bottom fluid movement. They are most commonly used for blending and solid suspensions because these applications often use vertical, cylindrical tanks that tend to create swirling patterns, regardless of the type of impeller being used. The flow pattern illustrated here shows that the use of baffles results in excellent topto-bottom circulation and great radial mixing.

FIGURE 2. Mixing in a baffled cylindrical tank

Baffle Configuration Baffles should be designed using the following guidelines (Fig 3): 

  

Number of baffles = 3 to 4 (4 is ideal, but 3 will result in sufficient mixing). Adding any more than 4 baffles will not result in any significant mixing improvement. Width = 1/12 of the tank diameter (i.e. for a 12’ diameter tank, the baffle width will be 1’)* Length = starts approximately 6 inches from the bottom and ends just above the maximum liquid level Mount Position = 1/6 of the baffle width off the tank wall**. (i.e. a 1’ wide baffle will be mounted 2” off the tank wall)

* For medium viscosity mixing (ie. viscosities over 3,000 s or Reynolds Numbers from 10 to 10,000), we often reduce the width of the baffle to 1/2 of standard width ** When agitating slurries, baffles are often located up to 1/2 of their width from the vessel wall to minimize accumulation of solids on or behind them.

FIGURE 3. Standard baffle design

Going Baffle-less There are instances where baffles are not required 



Square or Rectangular Blending Tanks: Most blending applications that use square/rectangular tanks don’t need baffles because these tanks are selfbaffling. However, they are less suitable for solid suspension because “dead spots” are formed in the corners. High Viscosity Mixing: For high viscosity mixing (viscosities over 5,000 s or Reynold’s Numbers < 10), the same power is consumed by the impeller, with or without baffle, so they’re seldom used.

Mixer Mounting Offset Angle Mounting With axial-flow impellers, an angular off-center position where the impeller is mounted approximately 10-15° from the vertical, can be used (Fig. 4). It’s worth noting that the angular off-center position used with axial impeller units is usually

limited to those delivering 3 HP or less. The unbalanced fluid forces generated by this mounting can become severe with higher power.

FIGURE 4. Offset angle mounting

Offset Vertical Mounting If an angle mount is not available, the mixer can be offset while being placed vertically in the tank. The rule of thumb for this is to offset the mixer on the x-axis, 1/6th of the total tank diameter. So, for a 60″ diameter tank the mixer would be offset 10” from center (60”/6 = 10”).

FIGURE 5. Offset vertical mounting

As you can see, baffle configuration and mixer mounting have a significant impact on the mixing process. When engineered correctly, the right application of these techniques can decrease costs & increase equipment life while optimizing the mixing process.