Are centrifugal compressors/turbines less efficient internally, and if so, why?

Question

From my related question which found a good example of a centrifugal turbine jet engine, the Henkel Hes 3.

Picture Source Website (it's in Czech). Thanks to Jan Hudec for finding it.

My understanding of centrifugal engines is that they have larger diameters and therefore larger nacelle drag, and therefore aren't favored.

So in this question, I want to ask, are centrifugal engines less efficient internally? That is, for a given thrust at given conditions, will the centrifugal have more, less, or equal fuel consumption than a "normal" axial-flow engine?

I can't imagine that friction of air flowing around a winding path, or related viscuous effects, could amount to any noticeable penalty. But I can't think of any other reason why centrifugals would be internally less efficient.

Note, another related question, one answer did say that centrifugal compressors will have higher losses than axial compressors, for a given compression ratio, but did not explain why.

Answer 1

Internally the big difference is that with axial compressors, it's easy to have a multi-stage compressor to give considerably higher overall compression.

While it is possible to link centrifugal compressors together into a multi-stage engine, it's considerably less common, so most centrifugal compressor engines are limited to the compression they can get from one stage (usually around 4:1).

Axial flow engines get lower compression per stage (usually around 1.2:1), but it's easy to have multiple stages, so engines with 10-15 (or so) stages are fairly common. Given the difference in compression per stage, an axial flow engine typically needs about 8 stages to produce higher overall compression than a single-stage centrifugal compressor.

It is also possible to combine the two. At least to my knowledge, the most common layout in this case is multiple axial-flow stages, followed by a single final stage using a centrifugal compressor.

Here's one paper about using a final centrifugal compression stage, in case you care: https://doi.org/10.2514/6.2019-0944