What is the purpose of those casing treatments and how were they designed?

Question

The images show a kind of casing treatment used in Russian aero-engines.
From what I have found out the first engine featuring this kind of casing treatment was the Tumansky R-13. Since then it was used in numerous Russian jet-engines (e.g. Tumansky R-29 or Klimov RD-33).

Casing treatments are usually used to increase the operating range of compressors. And there exists a wide range of different types/geometries of casing treatments:

I was not able to find any documentation or publication on the working principle of the Russian casing treatments and how they were designed. Since they were designed in the 1950s their design was likely done by correlations. The interesting thing is that the design of the 1970s looks very comparable so the advances in 1. computing power and 2. operating experience did not change them.

Does anyone have information on:

1. The design rules for these casing treatments (stagger angle, skew angle, axial position)?
2. The working principle or intent (recirculation, blowing, sucking)?

Answer 1

The casing treatments shown work by providing an alternative path for the rotor tip leakage flows; which otherwise collect at the rotor tip when highly loaded and block the flow resulting in a surge.

The lack of change is because there was no significant improvement in computing power between the 50s and the 70s that would help with such designs, (in fact it is only very recently that the flows can be accurately modelled.) and the cost of the experiments required to substantially iterate the design would be prohibitive.

The difference in designs is partially driven by parallel development, partially by patent avoidance, and partially the desire to minimise the impact on the compressor's components and its efficiency.