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What form does the discharge stream of a propeller take in a Herschel-Bulkley fluid, chracterised by having a certain yield stress, shear between layers only occurs beyond that stress.

This situation is known from biogas-plants, where the slurry is often mixed by propellers - Almost always in cylindrical tanks, with the propellers mounted so that they create a horizontal circular flow. Generally speaking, noone in the industry knows the viscosity of their slurry (measuring the flow-characteristics of liquid cow manure with gras in it is hard).

The following phenoma have been observed:

A long jet, accompanied by a flow of entrained liquid

A 'cavern' with a jet and recirculation to the back/suction side of the propeller, no gloabal flow beyond the cavern

A cavern, the propeller suck material on front an back and pushes it outward radially

It is also a known phenomena that propellers downstream of another propeller work better (don't create caverns).

We have serveral variables, like min. yield stress, viskosity, diameter of propeller, revolutions per time of propeller, form of propeller ( like steeper blades), power of propeller

I think that the relation 'higher yield stress => more likelyhood of forming a cavern' is intuitivly right.

What other quantitative relations like that are there?

What conditions make the third form of flow more or less likely?

The general (and plausible) attitiude seems to be that large diameter, low number of revolutions create the most global flow for the least power input. What limits are there to 'bigger, slower' from a fluid-mechanic standpoint?

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