Page 113 - Fluid Mechanics and Thermodynamics of Turbomachinery

94 Fluid Mechanics, Thermodynamics of Turbomachinery

FIG. 4.1. Turbine stage velocity diagrams.

The continuity equation for uniform, steady flow is,
1 A 1 c x1 D 2 A 2 c x2 D 3 A 3 c x3 .

In two-dimensional theory of turbomachines it is usually assumed, for simplicity,
that the axial velocity remains constant i.e. c x1 D c x2 D c x3 D c x .
This must imply that,
1 A 1 D 2 A 2 D 3 A 3 D constant. (4.1)

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), or,

W D P W/ Pm D h 01 h 03 D U.c y2 C c y3 /. (4.2)
In eqn. (4.2) the absolute tangential velocity components (c y ) are added,soas
to adhere to the agreed sign convention of Figure 4.1. As no work is done in the
nozzle row, the stagnation enthalpy across it remains constant and
h 01 D h 02 . (4.3)
1
2
2
Writing h 0 D h C .c C c / and using eqn. (4.3) in eqn. (4.2) we obtain,
2 x y
2
1
h 02 h 03 D .h 2 h 3 / C .c 2 c / D U.c y2 C c y3 /,
2 y2 y3