Nozzles
Diffusers
Diffuser pressure recovery
An ideal diffuser would recover the stagnation pressure, but practical diffusers cannot bring the fluid velocity to zero and have losses. The pressure recovered by such a diffuser is:
πd = pt2 / pt0
Shocks
The total temperature across a shock remains constant but the total pressure is lost.
Normal shock
The Mach number M2 after the shock is:
The density & velocity relation
the pressure relation
and the temperature relation
Inclined shock
Velocity triangles
Basic analysis of the effect of the blade rows on the airflow can be done through velocity triangles. The figure below shows a basic set of velocity triangles for compressor and turbine rows.
In the compressor the airflow is decelerated (diffused) in the velocity frame of the blade cascades. If the velocity of the inflow is u in the static frame then the rotor blades see the vector sum of u and ωr which is the velocity of the blades whirling at angular speed ω at that particular radius r. The rotor blades turn the flow incoming in the rotor frame of reference at velocity vri and diffuse it down to velocity vre. The stator sees the incoming flow at ure and diffuses it down to use and turns it back to the axial direction. The typical axial Mach number is around 0.6 and the rotor angular Mach number (ωr/a) is kept as high as possible to maximize the compression per stage. Since the fundamental gas dynamic process in the compressor is subsonic and supersonic diffusion, the limitations are imposed by the boundary layers and adverse pressure gradients which amplify them. The ultimate limit of compression is when the boundary layer diverges on the suction side of the blades and the blade row stalls.
The velocity triangles for compactness can be combined as shown on the right side since the angular velocity of the blade row is equal at inlet and exit.
In the turbine the airflow is accelerated (nozzled) in the velocity frame of the blade cascades. The incoming flow is accelerated and turned by the stators (nozzle vanes) to velocity uri and directed towards the turbine rotor. In the rotor frame of reference the flow comes in axially (or nearly so) at velocity vri and is accelerated and turned to velocity vre. The exit velocity ure then is nearly axial once the angular velocity ωr of the turbine blades is subtracted.
The turbine’s degree of reaction is the kinetic energy that occurs in the turbine rotor compared to the total kinetic change. The triangles above describe an approximately 50% reaction turbine. Impulse turbines have the rotor frame velocities vri and vre changing only in direction indicating that inlet and exit incidence angles of the blades are equal in magnitude if the axial velocity does not change.