Throughput number

The power input in stirred tanks can be calculated using the equation P = Ne pnM if the Newton number Ne, which at present still has to be determined by empirical means, is known. For stirred vessels with full reinforcement (bafQes, coils, see e.g. [20]), the only bioreactors of interest, this is a constant in the turbulent flow range Re = nd /v> 5000-10000, and in the non-aerated condition depends only on geometry (see e.g. [20]). In the aerated condition the Newton number is also influenced by the Froude number Fr = n d/g and the gas throughput number Q = q/nd (see e.g. [21-23]). 

The results of these model experiments are described in detail in Reference 7. For our consideration, it is sufficient to present only the main result here. This states that, in the industrially interesting range (Re > 10 and Fr >0.65), the power number Ne is dependent only on the gas throughput number Q. When the gas throughput number Q is increased thus enhancing gas hold-up in the liquid, the liquid density diminishes and Ne decreases to only one-third of its value in non-gassed liquid. 

One only needs to know—and this is essential—that the hydrodynamics in this case are governed solely by the gas throughput number and that the process is described by an unknown dependency Ne (0. Then one can calculate the Q number of the industrial plant ... 

In this representation, the throughput number Q is standardized by the intercept Ai. It is the numerical value of Q where the screw machine is conveying without pressure formation. With this kinematic flow parameter, h = QlAi, the state of flow of a screw machine can be outlined more distinctly. 

Throughput Number of samples that can be run in a given time period... 

Two screw profiles that are described by the same geometric parameters are known as geometrically similar. They can be converted into one another by scaling. The pressure and power numbers are dependent only on the throughput number if the screws are geometrically similar. The relationships are linear in the case of fluids of constant viscosity ( Newtonian fluids ). The complete pressure and energy behavior of a class of geometrically similar screws can thus be traced back to a simple linear relationship. 

The throughput number is simply the machine s output per revolution in a dimensionless form. This is related to the volume of the machine, as represented by the diameter to the power of three. The displaced volume of a screw machine is scaled with DJ, so this gives a parameter that describes the flow status independently of the machine size. 

Q-1 represents the reciprocal value of the well known gas throughput number Q. Fr is the Froude number, here formed with the gas throughput and cT is the dimensionless concentration (in ppm) of the foaming agent in the liquid. S are the physical properties which affect foam stability. Because they are neither known by number (i) nor by kind, instead of S the type of the foaming agent (name and chemical structure) must be given. 

III is named the gas throughput number Q, Yl2 is the inverse Reynolds number and 113 is the inverse Froude number. The gas throughput characteristics of a hollow stirrer then reads ... 

Testing is potentially adaptable to high throughput Number of animals is reduced Costs are decreased... 

The experimental data with 3-MIG stirrer in viscoelastic aqueous solutions of PAA (see bottom graph in Fig. 2.9) proved the above-mentioned expectation, that stirrers with a few paddles with low heights barely allowed the formation of gas cushions and as a result the Ne(Ga) dependence was only marginally affected by the gas throughput number Q. 

The most important boundary condition for the application of the proposed power characteristic Ne(Q, Fr, D/d, h/d) is however given by the upper boundary value of the gas throughput number Q. Each stirrer can, namely, at a particular stirrer speed only disperse a particular maximum gas throughput in the liquid. Upon exceeding this value the stirrer is flooded by gas i.e. it is completely enveloped by gas and is incapable of dispersing it. 

Thereby the discharge of the gas dispersion is also diminished, the gas cushions becomes ever larger and at a particular value of the gas throughput number Qmax the stirrer is flooded with gas. 

In order to be able to determine reliably the upper value of the gas throughput number, experiments have been carried out at different but constant stirrer speeds such that the air throughput was initially slowly increased until flooding occurred. Then the gas throughput was slowly reduced and the value at which the dispersing effect of the stirrer was restored noted [612]. 

Tab. 8.1 Liquid throughput number Qt as a function of the number of stages z in the mixing column with turbine stirrers (h/d = 0.33 D/d = 0.5) from 547] number of stages z 2 3 4 5...

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