Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

190 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 6.6. Flow angle and Mach number distributions with radius of a nozzle blade row
designed for constant specific mass flow.
(6.29)
Using the above set of equations the procedure for determining the nozzle exit flow
is as follows. Starting at r = rm, values of c m, a m, T m and r m are assumed to be known.
For a small finite interval Dr, the changes in velocity Dc, density Dr, and temperature
DT can be computed using eqns. (6.27), (6.28) and (6.29) respectively. Hence, at the
new radius r = rm +Dr the velocity c = cm +Dc, the density r = rm +Dr and temperature
T = Tm +DT are obtained. The corresponding flow angle a and Mach number M
can now be determined from eqns. (6.26) and (6.28a) respectively. Thus, all parameters
of the problem are known at radius r = rm +Dr. This procedure is repeated for
further increments in radius to the casing and again from the mean radius to the hub.
Figure 6.6 shows the distributions of flow angle and Mach number computed with
this procedure for a turbine nozzle blade row of 0.6 hub–tip radius ratio. The input data
used was am = 70.4 deg and M = 0.907 at the mean radius. Air was assumed at a stagnation
pressure of 859kPa and a stagnation temperature of 465K. A remarkable feature
of these results is the almost uniform swirl angle which is obtained.
With the nozzle exit flow fully determined the flow at rotor outlet can now be computed
by a similar procedure. The procedure is a little more complicated than that for
the nozzle row because the specific work done by the rotor is not uniform with radius.
Across the rotor, using the notation of Chapter 4,
and hence the gradient in stagnation enthalpy after the rotor is
(6.30)