Forty years ago I worked on engines with water jets in the front frame for the purpose of compressor cleaning. At that time we used a petroleum-based solvent mixed with the water, injected it while cranking on the starter, then let it soak a while to soften the deposits. Then crank it again while spraying demineralized water to flush the flowpath.
As NSEU says, the improvement was noteworthy.
The cleaner solvent was later decreed unfriendly to the environment, and a new protocol was developed, but I don't have those details at hand.