I can't find anything on the web about the Concorde's Snecma engine fan blade tip speed at full thrust. Any ideas?
Apart from the fact that the Rolls-Royce/Snecma Olympus 593 engines were pure turbojets so they did not have any fan, it's pretty easy to calculate (better approximate) the tip speed of the first Low-Pressure Compressor's wheel.
- The Olympus 593 had a diameter of about 1.2 meters [Wikipedia]. Let's say the first compressor wheel had a diameter of about 1 meter.
- As we're talking about the LP Compressor, we're interested in N1 speed. At 100% N1 speed, we are at 6500 rpms [FAA Type Certificate No. E20EU] (for N2, at 100%, 8530 rpms).
- Now it's just math to calculate, or, just use an online converter.
The result, as DoRoCro already wrote in his answer, is about 340 m/s.
As a first approximation, about Mach 1 (for the incoming air at the fan blade row, depending on temperature in turn depending on altitude) - any higher and you generate shock waves off the blade which inhibits the flow. The blade tip might be slightly above this so that some of the outer part of the blade is supersonic, but outside my knowledge when it comes to design of transonic compressors, but my guess is given the age that the design was subsonic.
(Remember that the job of the intake is to slow the incoming supersonic airflow down to speeds that the compressor can handle, at the same time boosting the pressure of the air ahead of the first fan stage)
http://www.saveconcordegroup.co.uk/engines/ suggests axial flow at the engine face is about 0.49 Mach