For many engineers and scientists in the chemical process industries, mixing is an essential unit operation. Often, this essential process conversion step between the raw materials and the final product uses a stirred tank. As important as this step can be, actual mixer performance often is poorly understood.
Everyone wants uniform mixing, but each process involves different fluid properties and operating variables that establish the mixing intensity needed to achieve uniformity. Fluid properties such as density and viscosity, impeller type, tank size and other characteristics all influence mixing intensity. By gaining an understanding of a mixer's process capabilities, you will be better able to apply existing equipment or design new equipment for a specific process. It also is important ," but difficult ," to know how to describe the required amount of mixing.
Several steps are key to developing a better understanding and to defining the mixing capabilities of a mixer. Some steps such as creating a scale sketch or drawing are simple. Other steps that determine mixing intensity require some knowledge and definition of the basic mixing processes. In addition, equipment design involves mechanical consideration of shaft strength and critical speed. Occasionally, the situation could be sufficiently unique to defy simple description.
Is that drawing accurate?
Some aspects of mixer description such as the dimensions of the mixer are almost intuitive. A common assumption is that all computer-aided design (CAD) drawings are to scale. Unfortunately, the drawings supplied by equipment manufacturers often are general-purpose drawings with specific numerical dimensions. Even when a drawing appears to show mixer impellers that are evenly spaced and the same size, the dimensions might reveal something entirely different.
One of the critical dimensions for any mixer is the distance between the lower impeller and the bottom of the tank. Because the mixer and tank often are purchased separately, communications about design changes to original dimensions might be overlooked.
Even if head dimensions and straight-side lengths are unchanged, changes to nozzle height or type can alter shaft-length requirements. In addition, mixer design includes mechanical considerations such as shaft strength and critical speed. Mixer shafts must be strong and stiff enough to avoid mechanical problems.
The most obvious and potentially disastrous problem is a mixer shaft that is too long to fit the tank. A less obvious problem is a shaft that is too short. A short shaft is easier to design mechanically, but it might mean the lower impeller is above or only slightly below the minimum liquid level for a batch process. In any case, a poorly positioned lower impeller can cause problems during tank filling or emptying operations.
The simple and effective solution to mixer and tank compatibility problems is a scale sketch or drawing. Fig. 1 shows an example of a scale drawing generated by CerebroMix Light II, a computer program from CerebroMix Inc., Campinas, Brazil.
Figure 1. Ensure Perfect Fit
A properly scaled drawing ensures that correct mixer shaft length and impeller sizes are chosen.
Visual observation often provides a clue to potential problems. You should draw the tank to scale, including nozzle-mounting dimensions. You then can draw the mixer inside the tank, with the impeller locations properly scaled. Finally, the liquid level needs to be shown so you can check for effective operation.
An often-overlooked consideration in liquid-level determination is the space occupied by the mixer, baffles and other tank internals. For mixers with common pitched-blade, straight-blade and hydrofoil impellers, designers generally can assume the internals occupy about 10 percent of the open tank volume. In other words, expect and plan for the liquid level to be about 10 percent higher than that calculated from the inside tank dimensions.
To adequately describe mixer size or characterize mixer capability, you must consider quantity, difficulty and mixing intensity.
The quantity of material to be mixed might seem to be an obvious characteristic because a large mixer will be required for a large quantity of material. Quantity can be expressed in terms of volume or mass. In any case, you must know the fluid density or specific gravity to determine mixer power requirements adequately; thus, volume and mass can be related.
The difficulty of a mixer application depends on the process characteristics. For fluid blending, viscosity is a natural difficulty parameter. The more viscous the fluid, the more difficult the mixing task. A large mixer will be required to mix a viscous fluid.
Particle-settling velocity and solids concentration are difficulty parameters for solids suspension. Gas flow rate is a difficulty parameter for gas dispersion. The difficulty parameters for other dispersion processes might involve combinations of density ratio, viscosity ratio, bonding characteristics, particle size and related factors.
The third mixing factor is mixing intensity. Unlike quantity and difficulty, which are associated with measurable characteristics, mixing intensity is an illusive characteristic. It often is described in general terms such as mild, medium or violent. However, some definitive quantification is needed.
Some years ago, an article describing liquid blending proposed a 1-to-10 scale for the quantification of mixing intensity.1 The article reduced the method to tabular form for typical applications.
With the huge increase in computing capabilities since then, programming those quantification methods is a logical extension to mixing analysis. The basic premise of the "scale of agitation" is that a value of 1 represents the minimum intensity necessary for complete motion of the liquid; a value of 10 represents the maximum practical intensity, although higher intensities might be used for extreme cases.
Within the range, values of 1 or 2 correspond to what might otherwise be called mild agitation. Values of 3 to 6 represent medium intensities, and values of 7 to 10 characterize violent agitation.
This 1-to-10 agitation scale is based on the impeller pumping capacity divided by the tank cross-sectional area, resulting in a bulk fluid velocity. This velocity, in feet/minute (ft/min.), then is divided by 6 to obtain the scale of agitation. Whatever the origin or justification for this mixing-intensity scale, the idea of a simple 1-to-10 range can be a useful method for describing mixing intensity.
The actual calculations for mixing intensity must account for several factors, not the least of which are the fluid properties, density and viscosity. In turbulent agitation, the power required to rotate the impeller is proportional to the diameter and rotational speed. As viscosity increases, flow patterns change, and fluid motion becomes more difficult.
The effect of viscosity on mixing intensity and impeller power can be related to an impeller Reynolds number. Just as in pipe flow, the Reynolds number is a dimensionless ratio of inertial forces to viscous forces. But unlike pipe flow, the impeller Reynolds number has different values. Turbulent conditions exist at impeller Reynolds numbers greater than 20,000, and laminar conditions are present for Reynolds numbers less than 10. The large range between these values describes the transition from turbulent to laminar flow.
Part of the difficulty plant personnel face in quantifying mixing intensity is the gradual transition in performance caused by increasing viscosity. The impeller pumping capacity or the ability to create mixing intensity decreases with increasing viscosity, which correlates to a decreasing Reynolds number. Combined with the reduced effectiveness of impeller pumping, the power required to rotate the impeller increases. This power also depends on Reynolds number.
Both relationships can be defined, but they usually are represented by curves on graphs. The analytical forms of these relationships are just curve fits of the empirical data. In any case, manual calculations are difficult and computer calculations are not easy to code.2
Add software; mix well
Even with these difficulties, a computer program is the logical answer for collecting and organizing the essential information. The dimensional information about the tank and mixer necessary for the scale sketch provides a basis for a mixing calculation.
Additional information about fluid properties and operating speed allows the calculation of mixing intensity. For example, the mixer in Fig. 1, operating at 100 revolutions per minute (rpm) in a fluid with a 1.1 specific gravity and a 150-centipoise (cp) viscosity, will create a mixing intensity of about 3.5 for liquid blending. This intensity, on a 1-to-10 scale, represents something in the low-to-moderate range. The impeller power is about 0.8 horsepower (hp), requiring at minimum a 1-hp motor.
For the same geometry and process conditions, an increase in the rotational speed to 250 rpm would increase the mixing intensity to 8.8 and require about 10 hp. A decrease in the speed to 37 rpm reduces the mixing intensity to 1.2, but requires less than 0.05 hp at the impeller. Computer software such as CerebroMix Light II provides a convenient means to calculate and test alternatives.
A computer program also can be used to design a mixer. Impeller diameters, operating speeds and other dimensional factors often fall into a general range related to tank dimensions. A mixer design can be developed to meet the requirements for a proposed mixing intensity and fluid properties. Even if the computer-generated design does not meet secondary requirements such as low liquid level, design revisions are easy with computer calculations.
For instance, you can design or evaluate a 36-in.-diameter tank with an American Society of Mechanical Engineers (ASME) torispherical head on the bottom filled with 150 gallons (gal.) of a 500-cp viscosity fluid. If defaults for CerebroMix are used with two three-blade hydrofoil impellers, the impellers with a 14.4-in. diameter are chosen. With a mixing intensity of 3.0, a medium intensity, a rotational speed of 185 rpm is recommended.
If you choose similar conditions with a non-Newtonian material, the computer program forces the impeller selection to be an anchor impeller. Although close-clearance impellers such as anchor or helical-ribbon styles often are used with high-viscosity fluids, they are not always necessary with non-Newtonian fluids. However, computer programs must be conservative to avoid possible misinterpretation.
Besides conservative impeller selections, computer programs place limits on other dimensions such as tank diameter, liquid level and impeller diameter. Fluid property characteristics such as density and viscosity more often are limited by application characteristics such as the Reynolds number, which takes into account a combination of mixer dimensions and fluid properties.
A practical example of a limitation on tank geometry selection is low liquid level. A 48-in.-diameter tank with a 36-in. straight side and dished heads provides an example. Although extremely low liquid levels often are sought in batch processes, you must choose limits to keep the mixing intensity calculations valid. In this example, the software places a practical limit of 311 gal. as the minimum volume. The straight-side liquid level is 16 in.
Liquid levels less than approximately one-third the tank diameter can be mixed, but the mixing intensity becomes less predictable. Although absolute limits cannot be placed on mixing in all cases, you must select practical limits to avoid significant errors in estimating mixer performance.
Perhaps the most important characteristic of a mixing intensity value is that you can use it to design mixers for specific applications. Many applications in several important process industries were defined in another article.3 Summarized in a table are descriptions of different applications, along with design criteria and typical mixing intensities.
The methods for establishing mixing intensity for other types of turbine impellers such as the hydrofoil impeller in Fig. 2 are the same as for the pitched-blade turbine used in the previous example. Some other impeller types, including an anchor impeller, are not as well established with respect to mixing intensity. However, power and mechanical design calculations still are important.
Figure 2. Blade Configuration Influences Mixing Intensity
Mixing intensity can be determined for many blade configurations besides common pitched-blade turbines, such as hydrofoil impeller (left). The calculations do not lend themselves to anchor impeller configurations (right).
Mind the mechanical design
Once process conditions are satisfied, you must evaluate the mechanical design. Shaft design must satisfy strength requirements to handle the torque required to turn the impellers, as well as the bending loads from random hydraulic forces on the impellers.
You can calculate torque by dividing the power by the impeller speed. You then can estimate random hydraulic loads on the impeller from the torque and impeller diameter, but you might require a service factor for certain applications. Impellers that operate near the liquid surface or in gas-dispersion applications might have hydraulic loads as much as three times that of typical liquid operation.
Another mechanical consideration is the natural frequency, also called critical speed, of the shaft. Natural frequency is more difficult to estimate than loads because impeller weights and support stiffness come into play. However, all mechanical requirements for a mixer can be estimated with software. By entering actual values for shaft diameter and impeller weights, you can achieve natural frequency calculations sufficiently accurate for general review.
By gaining an understanding of mixing capabilities and using systematic methods to design mixing equipment, you can improve engineering tasks. By defining mixing capabilities, you will be better able to document and evaluate existing equipment. Process changes or new operating conditions can be analyzed before the first batch is tried.
You can design new mixing equipment from scratch or evaluate equipment proposals from suppliers. Although computer-generated calculations are no substitute for experience, they lend guidance and can help you avoid obvious mistakes.
1. Hicks, R. W., et al. "How to Design Agitators for Desired Process Response," Chemical Engineering, April 26, 1976, pp. 102,"110.
2. Dickey, D. S. "Program Chooses Agitator," Chemical Engineering, Jan. 9, 1984, pp. 73,"81.
3. Hicks, R. W. and D. S. Dickey. "Applications Analysis for Turbine Agitators," Chemical Engineering, Nov. 8, 1976, pp. 127,"133.
Dave Dickey is senior consultant for MixTech Inc., Dayton, Ohio, and Souza is chairman of Cerebro Inc., Campinas, SP, Brazil. Reach them at 937-431-1446 and 305-592-6332 (U.S. office), respectively.