Humidity effect vs density on turbine engines
i do agree with you as humidity increase density decreases and that will have an impact in turbine engines as its works in the principle of thermal compression and expansions.
But turbine engines are designed to be over effecient on ground and idle powers so it dumps out all the air overboard.
during cruising altitude with lean air, it uses all the air compressed in its compressor stages, but it is still the combusion chamber and its turbine stage which does take all the load to propel the fan stage with its compressor. so it is also 100% driven by the turbine and combusion and any effect of humidity hence density would have an effect in the total performance.
variouse pressure and tempreture sensors fitted in the turbine engine which calculate and schedule the air and fuel mixture (air mixture is managed by altering the variable vanes in the compressor stages - fuel managed by fuel meetering unit) so the principle is the same for piston engines aircraft which shoud be fitted with turbo chargers to compensate for the decreasing air density.
thanks