Doppler requires droplets so that there is something upon which for the sound waves to reflect. No droplets if the steam is dry.
A similar concept is time-of-transit, but it works on dry fluids. There is an emitter on one side of the pipe. Upstream, on the opposite side of the pipe, there is a receiver, and an identical receiver the same distance downstream. The difference in time betwheen when a ping hits the upstream receiver and the downstream receiver is directly a function of the velocity, thus a function of the flowrate.