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I have that PDF on file, in the pictures you can see the impulse blading of the stators where there is no pitch on the blades except prior to the first stage and after the last. This type of axial compressor is inefficient but simple with the rotors acheiving ~80% of compression and stators just acting to guid the air flow.(reaction blading used on the HeS 30 and BMW 003D acheived roughly half of the compression at the stators) Only ~1.155:1 compresson per stage was produced, opposed to ~1.25:1 with a reaction compressor of the same time period (while centrifugal compressors could manage 2.8-4.0:1), this way the HeS-30 acheived the same compresson in 5 stages that the 004 did in 8 with resulting savings in weight, length, materials, and greater energy efficiency. The reaction compressor blades had to be machined and used thrust bearings, while the impulse blading of the 004 could be stamped, a rather inexpensive and efficient method.
I'm not sure what type of axial compressor the 003A/E used though, it seems to have been slightly more efficient (~1.18:1) than the Jumo but not by much, so possibly an impulse type as well. Encorporating a reaction type compressor (with the same number of stages) in the 003D raised thrust from 800 kp to 1,200 kp (a 50% increase!) and increased compression from ~3.2:1 to ~4.7:1 with little increase in fuel consumption or weight. (thus much better specicic fuel consumption) Just think, if the 004 had similar improvments 1300+ kp with nearly 6:1 compression should be possible!
There's also the "textbook" example of an axial compressor where most of the compression occurs at the stators: the rotors accelerating the air and the stators slowing it down, compressing in the process, and guiding it into the next stage. (like a difuser of a centrifugal compressor) I'm not sue of the name of this type of compresser though...