Gas turbine nozzle: principle and types

A nozzle is a passage of varying cross-section that converts the enthalpy (pressure energy) of a fluid into kinetic energy. From the steady flow energy equation for an adiabatic nozzle:

$$h_0 = h + \frac{C^2}{2} \;\Rightarrow\; C = \sqrt{2(h_0 - h)}$$

and for isentropic flow of a perfect gas the area-velocity relation is

$$\frac{dA}{A} = \frac{dC}{C}\left(Ma^2 - 1\right)$$

Area-velocity relation

Types

 Convergent      Convergent-divergent    Divergent (supersonic)
 ---\            ---\       /---            /---
 ====>           ===> throat ====>        ====>
 ---/            ---/       \---            \---

1. Convergent nozzle: the area decreases; the exit velocity is at most sonic. If the back pressure falls below the critical value ($p_b/p_0 < 0.528$ for air), the nozzle is choked: the exit pressure stays at $p^*$ and the further expansion occurs outside the nozzle through shock and expansion waves. Used on subsonic and low-supersonic aircraft engines, and as the final nozzle of turbojets.
2. Convergent-divergent (de Laval) nozzle: the flow is subsonic in the convergent part, $Ma = 1$ at the throat, and supersonic in the divergent part, where the pressure continues to fall. Used when the pressure ratio is high: rocket engines, afterburning and supersonic jet engines.
3. Divergent nozzle: a divergent passage with supersonic entry (the divergent part alone) accelerates the flow further. With subsonic entry it acts as a diffuser, used in engine inlets and compressor diffusers.

In gas turbines the turbine nozzle guide vanes form a ring of convergent passages that accelerate the gas and turn it onto the rotor blades; the propelling nozzle produces the jet thrust.