I think the latter picture quite elobately shows this. However, even then, the early gas turbines were not reaction turbines but impulse types. Müllers HeS030 was the first axial Reaction type gas turbine to my knowledge. This yielded significant improvements in efficiency of the engine.
Regarding the late ww2 german jet engine developments, I´d like to give some further thought on BMW projects.
BMW developed the P3302/3 into the BMW-003. By late 1940 they started another, initially preliminary project which would eventually end up in the large BMW-018 engine, of which at least two prototypes have been buildt, though evidence suggest that only the compressor has been trialed before the facilities were captured and the BMW-018V2 was destroyed (the -V1 was destroyed in oct. 1944 by an air raid).
However, Schelp went into the class II buissness with the HeS011 triggering the project in 1942. The RLM was not convinced that the diagonal compressor is necessarely the most efficient form of a class II jet engine and urged Schelp to order BMW to exploits it´s experiences in the more developed BMW-003C/D projects to scale the axial engine up into a suitable class II engine as a backup.
This was the late 1943 or early 1944 starting point of the BMW-P3306 projected jet engine. At wars end, the design of the BMW-P3306 V1 had been completed, though no parts have been assembled. The outlines of the projected engine read like:
diameter: 850mm
length: 3200mm
compression ratio: 4.0:1 (calculated)
thrust: 1700kp at 7500 rpm (calculated)
sfc: 1.15 (claculated)
7 stages axial compressor (reaction type)
1 stage axial turbine
annual compressor with 20 burners
Altough not run in ww2, one engine was made to this specification and trialed in march 1948. The head of the BMW jet engine project was hired by the french to set up a jet engine design bureau in sept. 1945. Just 3 weeks later, he presented to complete design of an engine "scaled up from the known BMW-003 and able to produce 1700kp". As You can imagine, he didn´t created this engine in three weeks in 1945, but what he was able to do is to recollect the complete set of ww2 BMW-P3306 drawings. He never referred to P3306 but I have a couple of drawings and it´s nothing else, it´s the realisation of the BMW ww2 jet engine.
The design was submitted and after the german design team signed a second contract in 1946, S.N.E.C.M.A. started preperation for part assembly of two jet engines, redesignated ATAR-101. The -V1 prototype was still a perfect BMW-P3306 with Riedel starter unit, hollow air cooled turbine blades from rather mild steel and adjustable exhoust area controlled by a jet needle. In the second prototype -V2 the mild steel was replaced by high Nickel and chromium content steels, resulting in simplier construction and increased rpm and allowed exhoust temperature.
Delays in S.N.E.C.M.A production (particularely in producing hollow turbine blades) made compressor parts aviable in late 1946 and in march 1948 the -V1 prototype was benchtested for the first time. It worked according to specification and developed 1700 kp thrust at 7500rpm as intended.
Just two months later, the-V2 became avaiable and produced 2,200kp thrust at 8,050 rpm. The following development of the ATAR-101A and -B (they removed the Riedel starter engine in the hub and changed the tail to exhoust eye-type lid shutters) is entirely post ww2.
In my mind, a much more reasonable engeneering approach than the HeS011. Note how much the inavaiability of proper heat resistent materials affected the performance of this engine.