文档介绍：Chapter 7. Scale-Up
Similitude
For the optimum design of a production-scale fermentation system (prototype), we must translate the data on a small scale (model) to the large scale. The fundamental requirement for scale-up is that the model and prototype should be similar to each other.
Two kinds of conditions must be satisfied to ensure similarity between model and prototype. They are:
(1) Geometric similarity of the physical boundaries:
The model and the prototype must be the same shape, and all linear dimensions of the model must be related to the corresponding dimensions of the prototype by a constant scale factor.
(2) Dynamic similarity of the flow fields: The ratio of flow velovities of corresponding fluid particles is the same in model and prototype as well as the ratio of all forces acting on corresponding fluid particles. When dynamic similarity of two flow fields with geometrically similar flow patterns.
The first requirement is obvious and easy to plish, but the second is difficult to understand and also to plish and needs explanation. For example, if force that may act on a fluid element in a fermenter during agitation are the viscosity force FV, drag force on impeller FD, and gravity force FG,each can be expressed with
characteristic quantities associated with the agitating system. According to Newton’s equation of viscosity, viscosity force is ()
Where du/dy is velocity gradient and A is the area on which the viscosity force acts. For the agitating system, the fluid dynamics involved are plex to calculate a wide range of velocity gradients present. However, it can be assumed that the average velocity gradient is proportional to agitation speed N and the area A is to D2I, which results.
()
The drag force FD can be characterized in an agitating system as
()
Since gravity force FG is equal to mass m times gravity constant g, ()
The summation of all forces is equal to the inertial force FI as,
= = ()
Then dynamic similarity betwe