Course 7 Learn the essence of the mixing Reynolds number

I’ve learned in the classroom that the word “characteristic” is used to indicated that the length, velocity, and others are those that are considered to be the most influential on the flow in the field of flow under consideration. In the case of a flow in a circular pipe, the characteristic length D is the inside diameter of the pipe, and the characteristic velocity U is the average flow rate in the pipe. I’ve also learned that the reason why the characteristic length is not the total length but the inside diameter of the pipe is because the friction resistance of the inner wall of the pipe greatly affects the flow.

Oops, the difference between viscosity and dynamic viscosity? Well ... (watching the textbooks in his school days) the dynamic viscosity is defined as follows:

In the field of mixing, viscosity μ is a property of the target fluid, and is “an index of difficulty of moving objects in the fluid”. Whereas, the textbook says that dynamic viscosity ν is “an index of difficulty of moving the fluid itself”.
It also says that what affects the difficulty of movement of the fluid is density, and if the density is different, also the difficulty of moving the fluid (dynamic viscosity) is different even if the viscosity is the same.

That's right. As shown in Figure 1, the characteristic length and characteristic velocity of the Reynolds number are different between those in circular pipes and those for mixing.

For the flow in a circular pipe, both the characteristic length and characteristic velocity seem to be selected relatively appropriately, but how for mixing? The characteristic length is the impeller diameter: d, and the characteristic velocity is the peripheral speed of impeller tips: U. It seems that the flow around the impeller tips is given more importance than that throughout the mixing vessel.

Yes! It is an important point that you need to be careful about when using the mixing Reynolds number!

The mixing Reynolds number is only a dimensionless number, which represents the flow around the tips of the rotating impeller and ignores the factors affecting the circulating flow throughout the vessel, such as the impeller width and the number of stages of impellers. Therefore, it is useful as a dimensionless factor when evaluating vessels with the same shape but different sizes, but it is no use comparing or discussing vessels having different impeller widths or numbers of stages of impellers by the mixing Reynolds number alone.

You have to be aware that a vessel with a single paddle impeller and a vessel with a double paddle impeller are quite different even the shape of the impeller is the same. Whereas, the Reynolds number in circular pipes is excellent as the index of flow because the cross-sections of circular pipes are always in a circular shape, and therefore geometrically similar.

I agree. Large impellers such as the MAXBLEND impeller can be regarded as “infinite multi-stage paddle impellers” in a sense. Also the reason why it is easier to scale up when using the MAXBLEND impeller than when using a conventional multi-stage paddle impeller may be because the mixing Reynolds number of the MAXBLEND impeller represents the flow throughout the vessel relatively well.