Thermodynamics of the axial turbine stage
The work done on the rotor by unit mass of fluid, the specific work, equals the stagnation enthalpy drop incurred by the fluid passing through the stage (assuming adiabatic flow). From the Euler work (Eq. (1.19a)), we can write
In Eq. (4.4), the absolute tangential velocity components (cθ) are added, so as to adhere to the agreed sign convention of Figure 4.3. As no work is done in the nozzle row, the stagnation enthalpy across it remains constant and
Thus, the relative stagnation enthalpy, h0;rel 5 h 1 ð1=2Þw2, remains unchanged through the rotor of a purely axial turbomachine. It is assumed that no radial shift of the streamlines occurs in this flow. In some modern axial turbines, the mean flow may have a component of radial velocity, and in this case the more general form of the Euler work equation must be used to account for changes in the blade speed perceived by the flow, see Eq. (1.21a). It is then the rothalpy that is conserved through the rotor,
where U2 and U3 are the local blade speeds at inlet and outlet from the rotor, U2 5 r2Ω and U3 5 r3Ω. Within the rest of this chapter, the analysis presented is directed at purely axial turbines that have a constant mean flow radius and therefore a single blade speed.
A Mollier diagram showing the change of state through a complete turbine stage, including the effects of irreversibility, is given in Figure 4.4.
Through the nozzles, the state point moves from 1 to 2 and the static pressure decreases from p1 to p2. In the rotor row, the absolute static pressure reduces (in general) from p2 to p3. It is important to note that all the conditions contained in Eqs (4.4)-(4.6) are satisfied in the figure.