Agitator Design for Gas-Liquid Fermenters and Bioreactors. Gregory T. Benz

elements of an agitator and tank may be seen there. A schematic view with components labeled and a few major nomenclature symbols may be found in Figure 3.2.

      An agitated tank consists of a number of elements and is dimensionally described by a number of symbols. We will go through these more or less in the order of power flow, referring to the nomenclature of Figure 3.2.

Prime Mover

Motive energy is provided to an agitator by means of a prime mover, which provides power in a rotary fashion. Usually, it is an electric motor, as shown in Figure 3.2. For fermenters, a variable speed drive is often provided, usually by means of a variable frequency drive (VFD), though other technologies are possible. In principle, many other rotary power sources could be used. Some that the author has seen used include air motors, DC motors, hydraulic motors, and even diesel engines. But, probably more than 99% of the time, the prime mover will be an electric motor.

Figure 3.1 Agitated tank.

      Source: Photo courtesy Chemineer, a brand of NOV. Permission granted by NOV.

Figure 3.2 Agitated tank sketch.

Reducer

      Most agitator designs do not operate at direct motor speed, except in very small tanks. The reducer decreases the shaft speed below motor speed and increases torque. In most agitator designs, the reducer must also support the weight of the shaft and impellers, the thrust due to tank pressure or vacuum, and the bending moment created by random fluid forces acting on the impellers. In some cases, those forces are supported by a separate set of bearings, and the shaft is flexibly coupled to the reducer.

      The two most common reducer designs in industry are belt drive and gear drive. Most fermenter agitators use gear drives. More discussion of drive types will be found in Chapter 17.

Shaft Seal

      Although not all agitators have shaft seals (some are mounted on open‐top tanks or basins), those used in fermenters almost always do. The purpose of the seal, in addition to maintaining tank pressure or vacuum, is to isolate tank contents from the outside environment. This may be done to keep foreign matter from contaminating the broth or to protect plant personnel from exposure to potentially harmful organisms or gases. Often, the shaft seal area is heated to create a sterile barrier. More information on shaft seals will be found in Chapter 15.

Wetted Parts

The power and torque from the reducer are transmitted to the tank contents by means of a shaft with diameter d, extending a distance L from the mounting flange. On the shaft are mounted one or more impellers of diameter D and actual blade width or height, W, located off bottom at a distance C. For this book, we measure C from the bottom edge of the impeller. Some other sources use the centerline of the impeller. We also define D as the flat‐to‐flat dimension of the blades in plan view, rather than the swept circle, called D_S. This makes a difference of about 1% in the calculated diameter for a pitched blade turbine of standard design, for example. This is illustrated in Figure 3.3, along with a few other relevant dimensions, such as the blade thickness, t_b.

      For multiple impellers, we would use subscripts such as D₁, D₂, C₁, and C₂.

Figure 3.3 Swept diameter.

Tank Dimensions

      The tank diameter is designated as T. The liquid level is designated as Z. Other tank dimensions, not shown on the sketch, could include head depths, straight side, nozzle projections, baffles (width, length, and offset from wall), and any relevant internals.

How Agitation Parameters Are Calculated

      Agitation systems, just as any other system producing or modifying fluid flow, must obey the laws of physics. In terms of mathematical models, they obey the equations of continuity and the Navier–Stokes equations. Unfortunately, those equations can usually only solve problems analytically in relatively simple geometries, such as flow in a pipe, and, often, only in laminar flow. Such equations can be supplemented by various turbulence models.

An agitated tank, however, is a very complex geometry. Most would agree that it is all but impossible to solve the equations of motion for an agitated tank by analytical methods. In modern times, there have been many successful attempts to model agitated tanks by using numerical methods, which in essence convert differential equations into a series of algebraic approximations. Those approximations can be very good, depending on the skill of the modeler and the computational power used. These methods are often called CFD (Computational Fluid Dynamics) and sometimes called CFM (Computational Fluid Mixing.) Chapter 14 describes some of the uses of CFD as applied to fermenter design.

      The traditional way of solving agitation problems is quite different. The approach that has been used in most studies, and which is still the staple of agitator design, is to use the equations of motion to derive dimensionless number groups and then correlate experimental data in terms of those dimensionless numbers. That is the approach we will take for the majority of this book.

      We will not show the derivation of the dimensionless numbers, but will describe the ones important for our use in designing agitators, and how they are used, especially for fermenter design.

      Some readers may be unfamiliar with the concept of dimensionless numbers, so we will give a brief description here, prior to getting into the commonly used dimensionless numbers.

      A dimensionless number is a ratio of quantities such that the dimensions and units in the numerator exactly match the dimensions and units in the denominator, thereby canceling all dimensions and units. The resulting dimensionless number has no units or dimensions; it is just a scalar number. It also does not depend on what units are used, though converting dissimilar units to a consistent set of units will assist with the math.

      A rather trivial example is the concept of aspect ratio of a cylinder, which equals its height or length divided by its diameter. A 5‐ft. tall cylinder with a 12 in. diameter has an aspect ratio of 5. That is because 5 ft. is 5 times as much, in terms of its dimension (length), as 12 in. But the math would be more obvious and less prone to error if we first converted the diameter to feet by dividing by 12, or, alternatively, converting the height of the cylinder to inches by multiplying by 12. But the important point is that it is the ratio of the actual physical dimensions and is not unit dependent. We could have stated the dimensions as meters, microns, or cubits; the dimensionless number we are calling aspect ratio would