Why doesn't the stagnation temperature change in a stator?

[granzer]

I am studying the rotary compressor and I have understood that the stagnation pressure and stagnation temperature both increase in the rotor stage (as energy is being added). I also read that in the stator stage the stagnation temperature remains a constant but there is loss of stagnation pressure. If there is a loss in stagnation pressure in the stator, shouldn't the stagnation temperature increase (I am guessing here that the stagnation pressure loss is converted into heat)?

 

[JBA]

Without seeing reference source, it is difficult to evaluate that statement. By the classical gas law formula, a reduction in stagnation pressure results in a reduction in stagnation temperature, not an increase.

 

[boneh3ad]

The flow is adiabatic in the stator stage, so there is no mechanism for increasing total temperature. In a compressible flow, there is a mechanism for viscous dissipation in the boundary layer that can dissipate some of the enthalpy, leading to what is called a recovery temperature, but this is a very minor effect compared to the overall enthalpy in the flow and is most important when trying to predict or calculate heat transfer rates into the surface. Otherwise, in general, the total temperature remains constant as long as the flow is adiabatic in that region.