This can only give you a general idea.

First of all, the blades of each stage of the compressor are divided into static blades and moving blades (not the fan you mentioned, that only has one stage of moving blades). The turbine works to drive the moving blades (which can also be understood as rotors) of the front compressor to rotate and compress the air entering from the air inlet. It doesn't mean that the speed of each stage is the same as you said. The compressor as a whole is a contraction channel, and the air volume becomes smaller after compression, which can only be said to be the same as the angular velocity at most. The angles (many angles) of compressor rotors in each stage are also different, which are mainly decided by designers, and many factors will be considered, not only the compression ratio (efficiency, space, anti-surge, cooperation between engine structures, etc.). ).

One more question. The compressor is boosted and decelerated. It is best to slow down to zero, and all the dynamic pressure is converted into static pressure (of course, this is almost impossible). It's not like you said to speed up.

The working principle of the compressor can be simply said that the moving blades play the role of compression. However, because the rotating blades (commonly used axial compressors at present) will make the air generate tangential velocity and cannot directly enter the next stage of moving blades for compression, the first stage of static blades is needed to make the air only move axially (the tangential velocity is zero). The role of the stationary blades is to ensure the compression efficiency of the compressor.

At present, the number of stages of military aero-engine compressors is about 6 or 7, and the total compression ratio is 25+. The compression ratio of the first few stages is very high, and the compression ratio of the last few stages is1.0x. The main reason is to ensure the efficiency and enter the combustion chamber with a stable flow field, thus improving the combustion efficiency. The civil engineering grade is greater than 10+, and the higher the total compression, the better. (This is related to the economy) There is 40+.

That's all I can say. I won't find a long article to post for you. If you want to know the working principle of aero-engine compressor from principle to design, you can find a book to read for yourself. The related topics are: working principle of turbomachinery, fluid mechanics and so on.