Page 288 - Fluid Mechanics and Thermodynamics of Turbomachinery

Radial Flow Gas Turbines 269
Ł
ratio with increasing  s reflecting the increase in nozzle flow area accompanying
the larger flow rates of higher specific speed. Figure 8.17 also shows the variation
of U 2 /c 0 with  s along the curve of maximum total-to-static efficiency.

Clearance and windage losses

A clearance gap must exist between the rotor vanes and the shroud. Because
of the pressure difference between the pressure and suction surfaces of a vane, a
leakage flow occurs through the gap introducing a loss in efficiency of the turbine.
The minimum clearance is usually a compromise between manufacturing difficulty
and aerodynamic requirements. Often, the minimum clearance is determined by
the differential expansion and cooling of components under transient operating
conditions which can compromise the steady state operating condition. According to
Rohlik (1968) the loss in specific work as a result of gap leakage can be determined
with the simple proportionality:

h c D h 0 .c/b av / (8.49)

where h 0 is the turbine specific work uncorrected for clearance or windage losses
1
and c/b av is the ratio of the gap to average vane height (i.e. b av D .b 2 C b 3 //.
2
A constant axial and radial gap, c D 0.25 mm, was used in the analytical study
of Rohlik quoted earlier. According to Rodgers (1969) extensive development on
small gas turbines has shown that it is difficult to maintain clearances less than about
0.4 mm. One consequence of this is that as small gas turbines are made progressively
smaller the relative magnitude of the clearance loss must increase.
The non-dimensional power loss due to windage on the back of the rotor has
been given by Shepherd (1956) in the form:
3 5 1/5
P w /. 2  D / D constant ð Re
2
where  is the rotational speed of the rotor and Re is a Reynolds number. Rohlik
(1968) used this expression to calculate the loss in specific work due to windage,
2
3
h w D 0.56 2 D .U 2 /100/ /. Pm Re/ (8.50)
2
where Pm is the total rate of mass flow entering the turbine and the Reynolds number
is defined by Re D U 2 D 2 / 2 , 2 being the kinematic viscosity of the gas corre-
sponding to the static temperature T 2 at nozzle exit.

Pressure ratio limits of the 90 deg IFR turbine

Every turbine type has pressure ratio limits, which are reached when the flow
chokes. Choking usually occurs when the absolute flow at rotor exit reaches sonic
velocity. (It can also occur when the relative velocity within the rotor reaches sonic
conditions.) In the following analysis it is assumed that the turbine first chokes when

Ł The ratio b 2 /D 2 is also affected by the pressure ratio and this has not been shown.