Stirrer diameter

P — power, V — volume, N — impeller speed, D — stirrer diameter, Source Biotechnology by Open Learning [22]. 

The critical feed time t it depends on the location and number of feed pipes, stirrer type, and mixing intensity, and increases with increasing reactor volume. When a constant power-to-volume ratio is preserved, ta-u is proportional to and where D., is the stirrer diameter and Vr the reactor volume (Bourne and Hilber, 1990 Bourne and Thoma, 1991). The productivity of the reactor expressed as the amount of product formed per unit time becomes almost independent of reactor volume. The reason is that the reaction goes to completion in the zone nearby the stirrer tip. The size of this zone increases independently of the tank size it only depends on the velocity of the liquid being injected, the location of the nozzle, and the stirrer geometry and speed of rotation. Accordingly, for rapid reactions, the feed time will also be the reaction time. 

The blend time increases significantly with reactor size. To keep the average energy dissipation constant one has to decrease the speed of rotation. However, as the stirrer diameter increases, the tip speed becomes greater despite the lower rotation speed. In this situation energy dissipated in the vicinity of the stirrer increases with reactor size. 

There is a parameter necessary to describe the abrasion resistance of each crystalline substance. This abrasion resistance must be correlated with parameters of the power input devices such as pump or stirrer diameter or the stirrer tip speed. The abrasion resistance of the crystalline particles produced by secondary nucleation in industrial crystallization processes is therefore a physical property of the substance. So far there is no physical property known containing all information about this abrasion resis-... 

In Figure 11.2 a schematic view of a stirred vessel is given. The vessel is cyhndrical with a height (m) and a diameter T (m). Usually is equal to or greater than 2 T. It is equipped with a stirrer in the lower compartment. TTiis stirrer is mounted near the bottom, usually at a distance equal to the stirrer diameter. At a lower position the stirrer and bottom interact, leading to a decrease in power consumption. At a higher position hquid circulation problems can occur because, at increased gas flow rate in case of aeration, the bubbles will not be recirculated in the lower compartment. Sometimes the upper compartment (s) are also equipped with a stirrer. The vessel is equipped with baffles to prevent rotation of the contents as a whole. For aeration an air sparger is mounted below the stirrer. For mass transfer... 

The stirrer diameter was introduced as the characteristic geometric parameter in the above case. This is reasonable. One can imagine how the mixing power would react to an increase of the vessel diameter D it is obvious that from a certain D on, there would be no influence but a small change of the stirrer diameter d would always have an impact. 

The results in Figure 3 were acquired by changing the rotational speed of the stirrer and the gas throughput, whereas the liquid properties and the characteristic length (stirrer diameter d) remained constant. But these results could have also been acquired by changing the stirrer diameter It does not... 

Mixing time 6 necessary to achieve a molecular homogeneity of a liquid mixture—normally measured by decolorization methods in material systems without differences in density and viscosity depends on only four parameters, stirrer diameter d, density p, dynamic viscosity / , and rotational speed k ... 

In Example 5.1, the working out of the power characteristics of a stirrer in a Newtonian fluid is presented in detail. It is shown how a relevance list containing five parameters stirrer power P, stirrer diameter d, density p, and viscosity p of the liquid and the stirrer speed n... 

The relevance list of this task consists of the target quantity (mixing power P) and the following parameters stirrer diameter d, density p, kinematic viscosity v of the liquid, and stirrer speed ... 

From Equation (38), we learn that the minimum achievable mixing time corresponds to the square of the stirrer diameter bigger volumes require longer mixing times. 

A 2.5 m3 stainless steel stirred tank reactor is to be used for a reaction with a batch volume of 2 m3 performed at 65 °C. The heat transfer coefficient of the reaction mass is determined in a reaction calorimeter by the Wilson plot as y = 1600Wnr2KA The reactor is equipped with an anchor stirrer operated at 45 rpm. Water, used as a coolant, enters the jacket at 13 °C. With a contents volume of 2 m3, the heat exchange area is 4.6 m2. The internal diameter of the reactor is 1.6 m. The stirrer diameter is 1.53 m. A cooling experiment was carried out in the temperature range around 70 °C, with the vessel containing 2000 kg water. The results are represented in Figure 9.16. 

In the most important stirring operation - the homogenization of liquid mixtures - the convective transport of liquid balls (macro-mixing) is of predominant importance. Thus, this process depends to a large degree on space geometry and type of stirrer. It is influenced by the extensive parameters such as stirrer speed, n, and stirrer diameter, d. Here, the similarity with respect to fluid dynamics is given by Re = n d2 p/p= idem. 

In stirring, is represented by n 1, whereby n [T-1] stands for the stirrer speed. With d as the stirrer diameter, the Reynolds number then becomes ... 

Macro-mixing concerns the state of flow produced by the stirrer in the vessel. The stirrer generates primary eddies whose size is of the same order of magnitude as the stirrer diameter d. The macro-scale, A, is therefore given by A d. It is described by the hydrodynamical pi-numbers such as Re = n d2/v, Fr = n2 d/g, and the like. 

Compared with this, so-called surface aeration brings about a comparatively modest oxygen uptake. Therefore, it is important to very accurately measure and/or to use a larger model scale. The latter is advisable because the diameters of the full-sized surface aerators amount to d-r 3 m and, therefore, the scale factor surpasses i= 10, even if a relatively large laboratory stirrer diameter of dM = 0.3 m is used. 

Not until the extremely accurate measurements of Schmidtke and Horvat [55] were published and, thereafter, evaluated by the author in the same pi-frame (see Fig. 24), was it possible to guarantee that the sorption characteristic is not given by (kLA) =/(Fr). Now, it turned out that an additional pi-number (the Galileo number Ga = Re2/Fr = d3g/v2), containing the stirrer diameter, d, had to be introduced in order to satisfactorily complete the correlation. In plotting... 

The power consumption, P, of a given type of stirrer under the given installation conditions depends on the following variables geometric parameters stirrer diameter, d... 

For a given geometry of the set-up, the relevance list for this problem contains the power consumption, P, as the target quantity, the stirrer diameter, d, as the characteristic length and a number of physical properties of the liquid and the gas (the latter are marked with an apostrophe) Densities, p and p, kinematic viscosities, v and v, surface tension, a, and an unknown number of still unknown physical properties, S, which describe the coalescence behaviour of finely dispersed gas bubbles and by this, indirectly, their hold-up in the liquid. The process parameters are the stirrer speed, n, and the gas throughput, q, which can be adjusted independently, as... 

Kneule and Weinspach (1967) also measured the suspension characteristics of numerous stirrer types and agitated vessels. They found the optimum stirrer diameter d, and distance from the bottom H, to be given by dT/d, = 3.0-3.5 and Hj/d, = 0.3-0.5. The optimum shapes for the vessel bottom are hemispherical and elliptical a flat vessel bottom is unsuitable for particle suspension. For a vessel with an elliptical bottom, baffles, and a propeller stirrer installed at HJd = 0.2-0.8 pumping the liquid toward the floor, the constant b in Eq. (3.22) has the value b = 3.06. For a turbine stirrer with six paddles and Hj/d, = 0.3, the value is b = 1.21. In order to keep the particles in the same material system in suspension, the propeller stirrer must therefore operate at a rotational speed (3.06/1.21)1/2 = 1.59 times higher than a turbine stirrer of the same size. 

The above correlation indicates a strong dependence of kLaL on stirrer diameter and speed. 

The power required for a given stirrer type and associated vessel configuration depends on the speed of rotation N, the stirrer diameter du the density p, and the kinematic viscosity v of the medium. In vessels without baffles, the liquid vortex, and therefore the acceleration due to gravity, g, is immaterial, as long as no gas is entrained in the liquid. Thus, P = f(N, dt,p, v), and in the dimensionless form, Ne = /(Re), a relationship generally known as the power characteristics of the stirrer. Here, Ne = P/(pN3df) is the Newton or Power number, and Re s Ndf/v the Reynolds number. This relationship was described in Sections II and III for gas-liquid and gas-liquid-solid systems. 

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